I have some trouble with this expression. It's by itself, on a sticker, without anything else before or after. I know っぽい can mean "-ish" and that with なる it usually means "tend to become" but since there is no adjective here I don't get it. "Become something like" what?
(っ)ぽい is basically a suffix ("-ish"), but in very informal speech, it is sometimes used like a standalone adjective meaning それっぽい or "authentic-looking/-sounding", "believable", "plausible", and so on. For example,
It's not very realistic, is it?
In your case, the sticker means something like "it's becoming more authentic" or "(finally) this is like the real thing". Looks like this is a phrase from SLAM DUNK, so I assume it was originally said with sufficient context. For example, if this is said during a boring basketball game, it would be interpreted as "Finally, this is real basketball!". But you can use the same phrase when something different from your expectations has finally become exciting.