Is Rozier being a poor mans Kyrie a reach? I really believe their style of play and mentality is similar.
He's really nothing at all like Kyrie. Almost two completely different players.
Personality wise Rozier has a tough, physical mentality - closer to Marcus Smart then he is to Kyrie. He has an extremely high motor - always plays extremely hard on defence, frequently fights for rebounds in traffic over bigs, dives for every loose ball, etc.
Rozier is also a very wiling passer - at times I sometimes feel he's TOO unselfish - when he's on the court with higher profile players he often defers and passes off the ball, even if he has a mismatch or an open lane. I get the impression that he's trying too hard to not affect the status quo and to try and be a good teammate, not step on the toes of his fellow star Celtics. When the star players sit you can see his mentality change, and he starts to play much more aggressively (and tends to do better as a result).
Physically he is lightning quick, incredibly fast in the open floor, very strong (physically) and likes to play above the rim when the opportunity presents itself.
By comparison Kyrie shows little motor - rarely plays with effort on defence, rarely ever chases down a loose ball, never see him battling for rebounds. He's never seen a shot he doesn't like and any time he has a decent shot he's likely to take it rather then pass it. Physically he's not a standout run/jump athlete, although he is very quick (stopping on a dime, chancing direction, changing speeds, etc) and tends to use that combined with his ball handling to get by people. Plays almost exclusively below the rim.
Only similarities I really see are that both guys tend to elevate their game during the big moments, both are super clucth, and both can score in a variety of ways (though Kyrie is a much better shooter). Also neither is a traditional pass-first PG.
Otherwise, I think these are very different players. I'd consider Rozier to be more like a poor man's Derrick Rose (before the injuries), but with a better three point shot and greater defensive potential.