Special comments for Minecraft and Chel:

There's a lot you can do competitively for Minecraft (hunger games, bingo, something Minecraft monday-esque). If you're interested in having a competition in it, deciding what to actually do with it is priority.

Similarly, the Chel's have got a lot of options. I'm a PC guy, so I don't know enough about which ones have private lobby capabilities, so if you want another category, ELI5 and I'll add it.