Are you sure your web browser isn't renaming them to something? From these links, I get the following names:-

setup_the_elder_scrolls_v_skyrim_special_edition_1.6.659.0.8_(64bit)_(59094).exe
setup_the_elder_scrolls_v_skyrim_special_edition_1.6.659.0.8_(64bit)_(59094)-1.bin
setup_the_elder_scrolls_v_skyrim_special_edition_1.6.659.0.8_(64bit)_(59094)-2.bin
setup_the_elder_scrolls_v_skyrim_special_edition_1.6.659.0.8_(64bit)_(59094)-3.bin
setup_the_elder_scrolls_v_skyrim_special_edition_1.6.659.0.8_(64bit)_(59094)-4.bin
setup_the_elder_scrolls_v_skyrim_special_edition_1.6.659.0.8_(64bit)_(59094)-5.bin
setup_the_elder_scrolls_v_skyrim_special_edition_1.6.659.0.8_(64bit)_(59094)-6.bin

You click on the .exe and it installs. If the files you've downloaded look like they're right size but are just named wrong, then try renaming them to above. The .exe is the smallest 1MB sized file.

Edit: If you have some adblocker / NoScipt running, then whitelisting GOG may help.

This may sound like a stupid question, but...did you accidentally download the Linux or Mac files?

Edit: (not the Skyrim files, since I don't have that yet)

Windows:
en1installer0 --> setup_game_name_64_1.3.3_.exe
en1installer1 --> setup_game_name_64_1.3.3_.bin

Linux:
en3installer0 --> game_name_en_1_3_3_15778.sh

Mac:
en2installer0 --> game_name_en_1_3_3_15760.pkg

The first ones are what you get shown, if you simply hover over the files --> the second ones are the files downloaded.

The en1installerX names are the names given to the links of games you'll see if you hover over the download link. These names are then changed to ones given by AB2012 when you actually download them. I imagine this has something to do with the CDN network gog uses.

I don't know where the conversion happens, I'd assume it's on gog's end, but maybe a script is run and your slower machine can't run that script. Is the slower machine a particularly old one or maybe using an unusual browser?

What browser are you using? It's using the download path as the file name, which isn't supposed to happen.

Note that you can use GOG Galaxy solely for downloading offline installers. You can find them in the Extras tab for the game in question. It's just one click to queue the entire batch of files for the base game, or each DLC. The filenames are supplied in an HTTP response header. So either the browser isn't naming the files correctly, or the correct information isn't supplied by the server. I don't own the game in question, but I'd wager it's the former.

First of all check your browser. When clicking a file, it should get it's real name.
"save as" might however provide the wrong name.

If you already downloaded everything, you can rename the files as shown above.

Don't worry about version numbers. The installer looks for files matching a certain name pattern
If your exe file is called "xxx.exe", it will look for "xxx-1.bin", "xxx-2.bin", "xxx-3.bin", ...

Are you perhaps using a download manager? Some download managers have trouble getting the file names right. For example DownThemAll before the latest update named the files just as you got them.

Renaming them like AB2012 told you to do should do the trick, if the files were downloaded correctly and only the filenames got lost.

That done the trick thank you AB2012!

Thanks for all the help everyone as well :) I should have said (sorry was doing work stuff at the same time as asking