I can highly recommend War Of Rights. Multiplayer only American civil war fps.
You form a long line in a field with 20 odd men facing the enemy line. It takes around 25 seconds to reload your gun, while the enemy is firing at you.
“Gentlemen, take aim, steady, steadyyy, steadyyyyyy, FIRE!”
The whole team gets penalised if you die out of line or duck for cover.
Matrix seems a bit overkill. I think they would be better off with something like gotify.
Take a look at dontkillmyapp.com to see if your phone provider hinders your messages.
There is unified push as Google alternative as well, which works with the schildichat matrix client.