This seems like a semantic discussion, rather than a philosophical one. Creating self-help frameworks based on mindfulness exercises and calling it Buddhism is like creating a stretching routine and calling it yoga. People will do it, and you'll end up with all the trappings of a self-help program, just like people have taken Buddhism and turned it into an established religion with all the trappings of religion.

The only thing I've seen that separates Buddhism from other religions, or at least that separates the underlying philosophy of Buddhism from the religious trappings, is that it actively encourages shedding those religious trappings. "If you meet Buddha on the road, kill him." Temples, shrines, rituals, dogma, etc. are all temporary and conditional, and therefore cause suffering. They exist as a framework to understand, but must then be overcome in the same way that we must overcome everything else. That doesn't mean the practice of it as a religion is any less mired in the same nonsense that all organized religion suffers from, but the source-code, so to speak, largely rejects treating it as a religion in the way we often think about religion.