Lots of great suggestions in here!
The General Video Game AI (GVGAI) environment has also just released their own Gym for training. With the competition set to run through CIG'18 in July 2018
https://github.com/rubenrtorrado/GVGAI_GYM/
IEEE Conference on Computational Intelligence and Games Competitions
https://project.dke.maastrichtuniversity.nl/cig2018/?page_id...
It's okay to start out small. It's not necessary to clone StarCraft to investigate high dimensional game state spaces. Remember it was a simple 2D board game like Go that was until recently considered unbeatable ;)
Take a look at games like Generals or Tron Light Cycles. Best of Luck!