Previously (a few years ago when I played it first time) worked but now it just doesn't start.
It sits in Task Manager (as x32 application) but does nothing and I don't even get splash screen.
Windows 7 (as it was before).

"Run as administrator" tried. I don't use Galaxy.

Found solution. Sorry for the trouble. Hope maybe it will help somebody else.
From the Reddit, courtesy to ThreeSon (as I cannot post the link):

"The best solution I know of is to modify the Windows registry so that Games Explorer points to a loopback address - meaning your own computer - instead of Microsoft's servers. I found this solution on GOG's troubleshooting page [which I wasn't able to find through search here – Lalai], who grabbed it from a user in their forums.

Here are the steps to take:

Open the Registry Editor. You can find it by searching for "Registry Editor" (without quotes) in the Start Menu.
In the left side of the Registry Editor, navigate to the following folder:

Computer\HKEY_CLASSES_ROOT\Local Settings\Software\Microsoft\Windows\GameUX\ServiceLocation

Create a backup by right-clicking the ServiceLocation folder and selecting Export.

Give it a name like "Games Explorer backup" (without quotes) and save it somewhere on your hard drive, in case you need to undo the changes.

Now in the right side of the Registry Editor, right-click Games and select Modify.

In the Value Data box, delete the current entry and replace it with 127.0.0.1

Then click OK and close the Registry Editor.

You may need to restart your computer for the changes to take effect."