Yes. Of course, YMMV. There will be groups and times that differ in just about any aspect of gameplay. For every time you can raise for your group not playing by the supported rules, I can raise an anecdote about how I saw a player staring at their sheet or flipping through a rulebook to find out what relevant action they could take in the situation. The anecdote-game takes us nowhere, mighty fast.
I must disagree. Where the anecdote-game take is the expectation that there is not one true way, one true result, and one true expectation. Different groups will approach the same game from entirely different directions. This is a fact that isn't entirely obvious without the anecdote game, and without the anecdote game you are likely to believe something that sounds good on the surface but is in fact ridiculous - like the system is singularly important in determining how a group plays a game.
So I don't disagree with your anecdote and the fact that you have an entirely different experience is entirely the point. If you feel that some aspect of role playing is missing from your game, changing systems in and of itself probably won't fix the problem. By Celebrim's Second Law of RPGs, what you must change is how you prepare to play and how you think about about playing. Sometimes system changes can induce that shift, and other times it requires the storyteller lead by example.
Except, of course, when it does. My FATE example comes up here - in the Spirit of the Century game I played in Tuesday, I was performing miserably in a combat, specifically because I was playing against type - I had a character whose personality and concept were about taking support actions. That's who he was. I was busy trying to directly harm the foe, and did poorly. As soon as I stopped, and started setting up other PCs for big strikes, I did swimmingly. In game terms, I started playing to my aspects, which help define the role you are playing.
Well, sure, broadly speaking any IC action you take while playing a RPG is 'role-playing', and rules can facilitate the experience of being in that role. But I think you are going to head for a contradiction here.
RPing is not limited to dialog. It is about the sum total of activity - it is about how the character approaches the world. The impatient barbarian who gets tired of all the talky-talk and starts the fight when he feels insulted is still role-playing. The steampunk mechanic who solves all problems with a gizmo, and doesn't talk for fight, is still role-playing.
If we want to talk about dialog alone, that's fine. But then the title of the thread should be "RPGs that focus on verbal interaction or social interaction between characters instead of combat".
Yes, but from the perspective that the impatient barbarian when he solves problems with combat is role-playing, and from the perspective that any in character action we take is also role-playing, then surely the OP should have titled the thread as you say without any irony, since otherwise the proper retort is "But combat is role-playing." I think we can understand the "role-playing instead of combat" in context to mean "IC dialog and social interaction instead of combat", because in the context of a RP game (and even outside of it) that's what 'role-playing' usually means.
By saying that the RPing is separate from the tactical combat game, I don't mean that the actions you choose to take in combat are unaffected by your character's personality much less your character's role. That at some level is ridiculous, since having more BAB as a fighter than a wizard would by that standard 'encourage playing your role' and 'encourage role playing'. At some level that is true, but then we could have a game that was exclusively tactical combat and claim it 'pushes the game toward role-playing' despite the only actions occurring being the management of the tactical combat game. What I mean by saying RPing is separate from the tactical combat game is that if I roll a d20 and say "I grip my battle axe in two hands and yell, "Taste my steel, green skinned vermin!", what I have said and communicated IC probably doesn't determine or influence the mechanical outcome of the attack proposition on the orc. I'm not more or less likely to hit the orc because I've imagined the action in IC terms. Simply saying, "I attack with my battle axe. 17, is that a hit?" is the same proposition. There are of course some exceptions where the designers were trying to push you to role play out that combat scene, but we can recognize that 'role-playing' is the something missing in that second naked metagame proposition and know that a rule is pushing toward 'role-playing' precisely because we generally equate role-playing with IC dialogue and interaction.