I don't know whether it makes them roleplay or not but it can put you into a different mindset. One is more "meta-level" thinking more about abilities and grid and mechanics, the other is more immersed in the actual game world, you don't think about mechanics but about actual situation. But YMMV, of course.
Again, you're probably seeing a phenomenon that's more about familiarity with the mechanics than the nature of the mechanics, themselves. We're simply much more viscerally aware of mechanics that we're unfamiliar with, while those that are second-nature can vanish below a sort of threshold of perception. Add a prejudice against one set of mechanics, or laboring against misinformation from those who do hold such a prejudice, and it gets that much worse.
And you can get interesting situations from both styles of play, one is more like playing Diablo or WoW, more tactical,the other is more cinematic and free-form.
It's more accurate to say that one is more cinematic, and the other is more free-form. Evoking a cinematic feel involves calling back genre tropes, and that's something that you can get a lot more of with a system that embraces and models those tropes, instead of leaving a blank space to be filled in, or, in a third extreme that we haven't touched on much in this thread, instead of simulating the processes implied by the set-dressing around them.
Another thing to think about is that 5e combines these two styles in one game. Most of the PC options do present the player with many choices from a wide variety of high-agency, discrete, precisely-defined, resource-managed effects (mostly spells, by a huge margin), and they are, of course, free to add imaginative flourishes or attempt 'creative' uses leveraging the wild range of things those effects can do. The few that do not get such options default to one mechanic, the attack, to make one sort of contribution to the party (DPR) in combat, with whatever spin or imaginative flourishes they care to append to it, and, of course, are free to attempt any 'creative' improvisations that a person might plausibly attempt.
Now, we could say that's 'the best of both worlds' or we could call it 'incoherent,' but it does just happen to be the way D&D shook out back in the day, too, and continued that way for a long time. And that familiarity counts for a lot in making it work.