I installed it via Galaxy, game starts, a window appears for a split second and then closes, and the galaxy informs me my games are being synched as if I exited.

I tried all the tips listed on the support page but nothing worked, anyone else having this problem? I'm running windows 7 still, but i played this game back in 2014 on this same PC with no issues.

Same here, I played it last time 3 months ago (before updating to Galaxy 2.0) and now doesn't launch anymore.

UPDATE: I had to Verify/Repair it from the client and that downloaded about 100+ MB and now it launched.

I just bought it yestersay, downloaded over night and installed today via GOG Galaxy 2.0.15 Beta.
On start I only get a black screen on monitor 2 (which isn't even set up as main monitor), the mousecursor shows as the known blue moving circle, then nothing until windows finally concludes that the WolfNewOrder_x64.exe stopped working.

Tried the repair option in GOG Galaxy, it too downloaded 128 MB of data, but at least for me it's still not working...

Edit:
So apparently i got it fixed after some research. By the looks of it there are really a lot of users having the same issue, the game starts into a black screen and then crashes, but weirdly tons of different solutions that helped, most of which sadly were related to AMD driver problems which were of no help to me as i'm on Nvidia.

But looking through my qconsole.log found in
C:\Users\'YOURID'\Saved Games\MachineGames\Wolfenstein The New Order
i found the following weird warning:
WARNING: Config file "wolfConfig.cfg" not found

Some more searching finally got me to a fairly old post from 2017 on the Steam forums
pointing out that you can create that missing config file yourself by opening Notepad or similar Editors, copying the following content:

configVersion 1
//========================================
bindset 6
unbindall
bind "JOY1" "_menuaccept"
bind "JOY2" "_menucancel"
//========================================
bindset 5
unbindall
//========================================
bindset 4
unbindall
bind "ESCAPE" "toggleMainMenu"
bind "W" "_moveforward"
bind "E" "_use"
bind "A" "_moveleft"
bind "S" "_moveback"
bind "D" "_moveright"
bind "J" "_inventory"
bind "M" "_map"
bind "JOY3" "_useandreload"
bind "JOY5" "_moveleft"
bind "JOY6" "_moveright"
bind "JOY9" "toggleMainMenu"
bind "JOY10" "_inventory"
bind "JOY_STICK1_UP" "_lookup"
bind "JOY_STICK1_DOWN" "_lookdown"
bind "JOY_STICK1_LEFT" "_lookleft"
bind "JOY_STICK1_RIGHT" "_lookright"
bind "JOY_STICK2_UP" "_lookup"
bind "JOY_STICK2_DOWN" "_lookdown"
bind "JOY_STICK2_LEFT" "_lookleft"
bind "JOY_STICK2_RIGHT" "_lookright"
bind "JOY_TRIGGER1" "_moveback"
bind "JOY_TRIGGER2" "_moveforward"
bind "JOY_DPAD_DOWN" "_map"
//========================================
bindset 3
unbindall
bind "ESCAPE" "toggleMainMenu"
bind "1" "_weap0"
bind "2" "_weap1"
bind "3" "_weap2"
bind "4" "_weap3"
bind "5" "_weap4"
bind "6" "_weap5"
bind "7" "_weap6"
bind "Q" "_togglefiremodeleft"
bind "W" "_moveforward"
bind "E" "_togglefiremoderight"
bind "R" "_reload"
bind "A" "_moveleft"
bind "S" "_moveback"
bind "D" "_moveright"
bind "J" "_inventory"
bind "M" "_map"
bind "LALT" "_covermode"
bind "PGUP" "_lookup"
bind "LEFTARROW" "_lookleft"
bind "RIGHTARROW" "_lookright"
bind "PGDN" "_lookdown"
bind "MOUSE1" "_attack1"
bind "MOUSE2" "_zoom"
bind "MWHEELDOWN" "_weapprevinv"
bind "MWHEELUP" "_weapnextinv"
bind "JOY3" "_useandreload"
bind "JOY4" "_prevequipweapon"
bind "JOY5" "_covermode"
bind "JOY6" "_quickgrenade"
bind "JOY9" "toggleMainMenu"
bind "JOY10" "_inventory"
bind "JOY_STICK1_UP" "_moveforward"
bind "JOY_STICK1_DOWN" "_moveback"
bind "JOY_STICK1_LEFT" "_moveleft"
bind "JOY_STICK1_RIGHT" "_moveright"
bind "JOY_STICK2_UP" "_lookup"
bind "JOY_STICK2_DOWN" "_lookdown"
bind "JOY_STICK2_LEFT" "_lookleft"
bind "JOY_STICK2_RIGHT" "_lookright"
bind "JOY_TRIGGER1" "_attack1"
bind "JOY_DPAD_UP" "_toggledualwield"
bind "JOY_DPAD_DOWN" "_map"
bind "JOY_DPAD_LEFT" "_togglefiremodeleft"
bind "JOY_DPAD_RIGHT" "_togglefiremoderight"
//========================================
bindset 2
unbindall
bind "ESCAPE" "toggleMainMenu"
bind "W" "_moveforward"
bind "E" "_use"
bind "A" "_moveleft"
bind "S" "_moveback"
bind "D" "_moveright"
bind "J" "_inventory"
bind "M" "_map"
bind "SPACE" "_sprint"
bind "MOUSE1" "_attack1"
bind "MOUSE2" "_zoom"
bind "JOY2" "_sprint"
bind "JOY3" "_attack1"
bind "JOY7" "_use"
bind "JOY9" "toggleMainMenu"
bind "JOY10" "_inventory"
bind "JOY_STICK1_LEFT" "_moveleft"
bind "JOY_STICK1_RIGHT" "_moveright"
bind "JOY_STICK2_UP" "_lookup"
bind "JOY_STICK2_DOWN" "_lookdown"
bind "JOY_STICK2_LEFT" "_lookleft"
bind "JOY_STICK2_RIGHT" "_lookright"
bind "JOY_TRIGGER1" "_moveback"
bind "JOY_TRIGGER2" "_moveforward"
bind "JOY_DPAD_DOWN" "_map"
//========================================
bindset 1
unbindall
bind "ESCAPE" "_menucancel"
bind "TAB" "_menutabtoggle"
bind "Q" "_menuextraaction"
bind "E" "_menualtaction"
bind "ENTER" "_menuaccept"
bind "JOY1" "_menuaccept"
bind "JOY2" "_menucancel"
bind "JOY3" "_menualtaction"
bind "JOY4" "_menuextraaction"
bind "JOY5" "_menutableft"
bind "JOY6" "_menutabright"
bind "JOY_STICK1_LEFT" "_movestick"
bind "JOY_STICK2_RIGHT" "_lookstick"
//========================================
bindset 0
unbindall
bind "ESCAPE" "toggleMainMenu"
bind "1" "_weap0"
bind "2" "_weap1"
bind "3" "_weap2"
bind "4" "_weap3"
bind "5" "_weap4"
bind "6" "_weap5"
bind "7" "_weap6"
bind "8" "_weap7"
bind "Q" "_prevequipweapon"
bind "W" "_moveforward"
bind "E" "_use"
bind "R" "_reload"
bind "A" "_moveleft"
bind "S" "_moveback"
bind "D" "_moveright"
bind "F" "_toggledualwield"
bind "G" "_quickgrenade"
bind "J" "_inventory"
bind "LSHIFT" "_sprint"
bind "Z" "_togglefiremodeleft"
bind "X" "_togglefiremoderight"
bind "C" "_crouch"
bind "M" "_map"
bind "LALT" "_covermode"
bind "SPACE" "_jump"
bind "F10" "devgui 1"
bind "F12" "screenshot"
bind "UPARROW" "_lookup"
bind "LEFTARROW" "_lookleft"
bind "RIGHTARROW" "_lookright"
bind "DOWNARROW" "_lookdown"
bind "MOUSE1" "_attack1"
bind "MOUSE2" "_zoom"
bind "MOUSE3" "_melee"
bind "MWHEELDOWN" "_weapprevinv"
bind "MWHEELUP" "_weapnextinv"
bind "JOY1" "_jump"
bind "JOY2" "_crouch"
bind "JOY3" "_useandreload"
bind "JOY4" "_prevequipweapon"
bind "JOY5" "_covermode"
bind "JOY6" "_quickgrenadeandweaponsel"
bind "JOY7" "_sprint"
bind "JOY8" "_melee"
bind "JOY9" "toggleMainMenu"
bind "JOY10" "_inventory"
bind "JOY_STICK1_UP" "_moveforward"
bind "JOY_STICK1_DOWN" "_moveback"
bind "JOY_STICK1_LEFT" "_moveleft"
bind "JOY_STICK1_RIGHT" "_moveright"
bind "JOY_STICK2_UP" "_lookup"
bind "JOY_STICK2_DOWN" "_lookdown"
bind "JOY_STICK2_LEFT" "_lookleft"
bind "JOY_STICK2_RIGHT" "_lookright"
bind "JOY_TRIGGER1" "_zoom"
bind "JOY_TRIGGER2" "_attack1"
bind "JOY_DPAD_UP" "_toggledualwield"
bind "JOY_DPAD_DOWN" "_map"
bind "JOY_DPAD_LEFT" "_togglefiremodeleft"
bind "JOY_DPAD_RIGHT" "_togglefiremoderight"
//========================================
vt_pageImageSizeUniqueDiffuseOnly "256"
vt_pageImageSizeUnique "8192"
r_initialMonitor "1"
r_mode "32"

into the text field, then save as WolfConfig.cfg and place that created configfile in the base folder within your Wolfenstein The New Order installation folder.
In my case this was G:\GOG\Wolfenstein The New Order\base

Shoutout to Dead Plc on steam, cheers mate and thanks for that tip!

I just experienced some related problem with my new RTX GPU running two monitors.
The game would start with a black screen and the audio playing.
I found that you need to adjust scaling options in the control panel or through the shortcut, however that did not fix it.

What eventually fixed the problem:
- Rename the game executable from WolfNewOrder_x64.exe to WolfNewOrder_x32.exe
- create a shortcut on Desktop
- right click on shortcut -> properties -> add -window to the path under "target"
- launch the game (you should get a picture now, probaly low-res)
- enter the game options
- switch from fullscreen to window
- adjust the resolution to your desired resolution (adjusting it while set to fullscreen will result in a black screen)
- switch from window to "fullscreen window" (for some reason, this disables the ability to change the resolution, so you need to adjust it while the game is windowed)
- enjoy

PS using Nvidia DSR also seems to mess up the game, so disable that in Nvidia control panel
PPS you may have to disable your second monitor, to do so, press Win+P and choose "PC Screen only"