It seems that you're using an outdated browser. Some things may not work as they should (or don't work at all).
We suggest you upgrade newer and better browser like: Chrome, Firefox, Internet Explorer or Opera

So I've been wanting to show this game to my son for some time now. And then it pops up on sale today. So I bought it and downloaded it, then installed it.

However, every time I click play from the GOG interface absolutely nothing happens. If I run task manager, it shows up there, but doesn't do anything else.

I'm running an intel core i3-4005U CPU @ 1.70 GHz with Windows 10. 64bit.

Right now I'm feeling very swindled.
You could try this:

Contacting Support is always an option:
Try alt tabbing into it or running it in a window.

Before you run off to support, read this instead.