I think you'd like the look of tile or wood better than carpet (even the less expensive "engineered" wood), and those would certainly last longer than carpet. However, if you go with tile, heed Mike's suggestion regarding an area rug. My own poker room (some less informed individuals have called it a "dining room") has tile, with a rug underneath the poker table. You don't want naked tile directly below the poker table, as clay chips dropped to a tile floor almost always suffer damage.
If I were re-modeling a basement poker room like you, I'd probably opt for wood.