On Steam the reviews are terrible, everyone is saying the game is full of glitches and crashes.
Seems the Gog version is as bad. BUT:
Since I don't buy games on Steam anymore I bought it here. Hell, I even pre-ordered it because I've wanted Telltale to make a Batman game since I completed their Borderlands spin-off. I completed the first season in one sitting with absolutely zero problems.

Windows 8.1 Pro x64
MSI GTX 980 Ti
i5 4690K 3.50 GHz
16 GiB DDR3

The only issue I've had so far with the game is lack of dialogue audio in certain (Mostly minor) parts but aside from that everything was working as intended.

I can confirm that the black screen after 'Press A to start" seems to have been introduced to the GOG build in the latest patch. The game was working for me prior to the update, but now I can't get past the intro screen.

Forgot to mention: the game still performs awesome after the patch.
I seriously can't be the only one with such luck. What have you people done with your PC's?

This is honestly speaking the first time ever I've had issues with a Telltale game. However, people seem to have loads of issues with Telltale games every time they launch a new game. I love their games, so I won't stop buying their games despite shitty user reviews, but they should probably wake up considering every launch of their games have been plagued by issues for many people.