As @Theo mentioned, game companies like to refer to a business model built around buying usability extras for a "free" game as "Freemium".
However, in the situation where the game doesn't really allow a player to make a competitive showing without purchasing stuff, we gamers call it Pay-to-Win (sometimes abbreviated as P2W). The name is always used derisively, so I doubt you'll ever hear a company adopt it in their game marketing.