I think jailbreaking your iPhone is the only way to track how many times you use specific apps.
Otherwise, you can get an idea of how often he plays specific games by splitting the games into different homescreens. This would work for the short-term.
For example, say you have homescreens 1 -> 2 -> 3. Let's assume that regular apps (i.e. Messages, Facetime, Contacts, other non-games) are on homescreen #1.
Initially, homescreen #2 will have just one app on it while all the games are on homescreen #3. Use homescreen #2 as a "recently used" homescreen. Every time he plays a game, he moves said app from homescreen #3 to the top of #2. Whatever games get left on homescreen #3 after, say, 2 weeks are worth deleting.