I haven't played Rust, but unless it has some sort class system, skill trees of some kind, or some sort 'stats' that get updated upon 'leveling' I would say no. Roleplaying games have at least 2-3 of those elements if not more.
If you cannot gain 'experience' points then definitely not. Although I suppose a new game mechanic could arise that doesn't use skill points. Real human beings don't have skill points. So I suppose Rust could evolve into some sort of hybrid. But that is a topic for another thread. So no. I stand by my statement.
I would classify Rust as a survival crafting fps with elements of an mmo.