Between 1051 and 1100 out of 1252 games on GOG (counting store titles, not library titles) should work on Windows 10, so I suggest you contact support.

EDIT: That is, between 83.839% and 87.879% of the currently sold games on GOG should be compatible with Windows 10, meaning more than 12.141% or at least 152 of currently sold game bundles on GOG are NOT (yet) necessarily compatible with Windows 10.

Is this the case for all the games you have tried so far? Are the games in question actually compatible with Windows 10?

It was atleast mentioned in the sidebar.
[i]"Works on:
Windows (XP, Vista, 7, 8, 10) "[/i]

This one for example.

Try right clicking and selecting "Analyze wait chain" (Warteschlange analysieren). If something irrelevant like Skype, Cortana or even Explorer is holding up the process, terminate it. See if that helps.

If it turns out to be Windows Explorer, you can always re-launch it from the Task Manager afterwards.

I see. Then it should indeed work. While you wait for some other Windows 10 users to reply, I would advise you to contact GOG's support for the game in question. To do so, click the game's box in your library, then the button "More" and it should show a drop-down menu; select support from there. Then take a look at the right side of the page and you should see a link that says "I can't find a solution for my problem". Click it and it should take you to the game's support page. There, you should describe the problem you are facing (as well as indicate that it happens to more than one of your games) and also send them a DxDiag report (instructions can be found here).

Thank you both!

The wait chain was empty, it said the ".exe is running normally."