Re: Plain text rudder commands is not a problem in itself
From a relative of mine who works offshore, yes, they often have consoles set up for gaming. There's also often a thriving film/tv piracy scene going on, where crew members swap videos back and forth to keep themselves occupied.
As for internet access, it depends. Usually these days they get enough for text based communications, and the odd picture. Some of the really fancy new boats have enough bandwidth to do VoIP (with a huge and almost unusable latency). For online gaming though you're pretty much limited to play-by-email.
I assume ships in places like the Channel can probably pick up on-shore mobile networks and get 3/4G coverage though.