The launcher starts...and that's it. I click play and it crashes. I bought this because the Steam version doesn't work. Well this does the same thing. Any thoughts?

Yeah. My thought is clearly you've proven across 2 different versions that by process of elimination that the game is not the issue, making the smoking gun some incompatibility on your own system, rather than the game itself.

Additional evidence : I am also running Win7 Pro and I've run *both* the Steam *and* the GOG versions with no issues whatsoever.

How to address that? That's a can of worms. You may have to take it up with GOG's tech support or ask a LOT of questions and have a back-and-forth discourse here.

Try installing the following redists:

VC++ 2008 SP1: https://www.microsoft.com/en-us/download/details.aspx?id=5582

DirectX 9 Redist: https://www.microsoft.com/en-us/download/details.aspx?id=8109

See if that works.

I've got that too (WIn7 Pro). I managed some how but there should be possible "easier" solution:
set windowed mode -> star the game -> close it -> change settings to full screen mode -> start the game

Problem solved?

It's usually the GPU that causes most of the issues. What do you have?