You half-can.
I say half, because there's two possible ways I can see running a text-based game. One involves a centralized server running in a language like c++ or c#, or one of the dozens of other languages available. This type can't run on x10hosting.
The OTHER way I can see doing it is via ASP.Net/PHP and an sql database, with minimal interaction between players. Think TribeWars, 1000 AD, or any of the other countless Turn Based strategy games playable in a browser. These you -can- run on x10, within limits - you'd run into the risk of running out of account space to store data, exceeding bandwidth if it gets popular, or if you need to run a Cron Job faster than once every five minutes.
So depending which type you're looking at, it -is- possible to run it on x10. Course, the one with the most options available is the one that -cant- run on x10's webhosting services (free OR paid), but if all you're looking for is a turn based strategy where everything boils down to math and luck, that could run on x10