Chrome may compete with Firefox, but Mozilla isn't a competitor for Google's profits or its core business.
As an analogy, consider Apple and Best Buy. Apple owns its own retail stores, and those stores are competition for Best Buy. But Apple isn't really in the business of retail; they have no reason to stop you from buying Macs and iPads at Best Buy. Retail is just a channel for Apple's real business, and its to their advantage to push their product through the channels they own and the channels they don't.
The browser is a channel for Google's core business of search advertising. Like Apple, they get some benefits from building and controlling a distribution channel of their own. But they have no motivation to stop pushing their core product to users of other browsers too.
As an analogy, consider Apple and Best Buy. Apple owns its own retail stores, and those stores are competition for Best Buy. But Apple isn't really in the business of retail; they have no reason to stop you from buying Macs and iPads at Best Buy. Retail is just a channel for Apple's real business, and its to their advantage to push their product through the channels they own and the channels they don't.
The browser is a channel for Google's core business of search advertising. Like Apple, they get some benefits from building and controlling a distribution channel of their own. But they have no motivation to stop pushing their core product to users of other browsers too.