Learn Dutch: Mijn broer is erg fanatiek, maar ik game niet meer. - My brother is very fanatical, but I do not play video games anymore.

You use geen ... meer when you no longer have or do something involving an unspecific noun (like 'I have no more time' - ik heb geen tijd meer). In this sentence, you are directly negating the verb game (to play video games). To say you no longer perform an action, you use niet meer.

Is game acting as a verb here?

Yes! Dutch uses the English loanword gamen as a regular verb meaning 'to play video games'. Because the subject is ik, it uses the stem game. For 'he' or 'she', it would be hij/zij gamet.

Does fanatiek have a negative meaning like 'fanatical' does in English?

Not necessarily. In English, 'fanatical' often sounds extreme or obsessive. In Dutch, especially regarding games or sports, fanatiek is very common and simply means being highly competitive, passionate, or driven to win.

Why doesn't maar send the verb game to the end of the sentence?

Maar (but) is a coordinating conjunction, just like en (and) or of (or). These words link two main clauses together without changing the word order. So, the second part follows the normal subject-verb order: ik + game.