I also have the steam version of AoE II with the expansions, have you or anyone managed to find a fix for this yet? I have only just updated to windows 10 and as it was a Microsoft game did not think it wouldn't work ! Any help appreciated.
OK just after I posted this my husband found a solution on another forum site, for the Steam version of AoE II HD Edition. It has worked for us so I hope this works for anyone else with the same problem.
Open up steam and find your game in your library
Right click on the game and go to properties
from properties go to Local Files
then click on Verify Integrity of Game Cache ....
this will take a few minutes to run, and you may get a error message at the end saying 1 file was unable to update, but don't worry about it, it still works.
Close this down then open up your game, you may find it stalls in the first screen and looks like its not working, but if you just click on the mouse (my mouse icon had vanished, but you can still just click it) it will go to the main game screen and should work as normal from there.
I know its not ideal but at least the game should now work. I hope it works for you as it has done for us.