One of the reasons people play RPGs is to (pretend to) do things that they can't in real life. If I picked up a sword, I'd have even odds of injuring myself more than the other guy; but, in an RPG, I can play a Fighter who wields a sword with aplomb. I may not be able to tell an enthralling story, but, in an RPG, I can play a Bard who can keep an audience enraptured for hours.
Player and Character skills are different. Requiring that players do "stuff" in the real world in order to activate their characters' abilities (aside from whatever the rules require) severely disadvantages players who are playing characters with strengths that don't overlap with their players'.
Note that this is different from encouraging the player to be specific in what they're trying to do. "I roll diplomacy against the guard" is different from "I try to imply to the guard that letting us through is for the greater good, even if it's technically against their orders"; the former is okay (for most people, at least some of the time) while the latter is great. The problem comes up when the GM requires the player to put that implication into words in order to roll Diplomacy (or uses the player's words to modify the result of the roll) - a player for whom subtlety is difficult shouldn't be punished for playing a character who can play people like fine violins.
I suspect that the player who is expressing resentment is feeling harmed (or, at least, limited) by having to try to do things in the real world in order for their character to do them in-game. You mentioned having the Bard sing a bit: I've got several friends for whom Bard would be entirely off-limits if they had to sing (well) to Inspire Confidence. If your resentful player wants to do awesome stuff in-game but feels that they can't do it well enough in the real world for their character to have a chance of succeeding, I can definitely understand their discomfort. I've run into that myself, especially in systems that explicitly reward stunting (describing the awesome thing your character is doing in order to get mechanical bonuses - the better the description, the better the mechanical reward). Every time I tried to stunt, I managed to get penalties because I couldn't explain what I was trying to do in just the right words for the GM to see it as a stunt; I hate stunting systems as a result.
Regarding the props: in my experience, a small handful of props can be really neat, but they reach the point of diminishing returns pretty quickly (your mileage may vary greatly on this one, though). If they're there for atmosphere, great; if they're there so that the players have to do "stuff" with them for their characters to do "stuff" in-game, they're typically a distraction at best (major exceptions exist, especially maps, and pre-printed copies of the riddle/puzzle's rules; riddles and puzzles are a whole 'nother kettle of fish, though). The more skill a prop requires to use, the worse its effect on the group will tend to be - goblets that the players can drink from are probably neat; a puzzle box that the players must open is likely to become more and more frustrating as its trick eludes the players (who wonder why the rogue, who's been opening locks left and right, can't just open this box, too).
Side-note: I think you're confusing metagaming with LARPing.
Metagaming is an "out of character" action where a player's character makes use of knowledge that the player is aware of but that the character is not meant to be aware of.
In this sense, metagaming is when players have read the monster manual - or even the adventure module or GM's notes - and act accordingly (eg., they know which lever to pull because they read ahead, not because of a skill roll or figuring out the puzzle; or, despite not recognizing a fey as such in-game, they reach for the cold-iron weapon that they've been carrying around for the last 3 levels because it'll get past their DR better).
There's another sense of metagaming in which the players will go to absurd lengths to support the underlying assumptions of the system (eg., that the party will stay together indefinitely, that the Paladin will put up with the Rogue's not-really-good-but-not-horribly-evil antics, etc.). It's the implicit social contract that the rules assume exists without explicitly stating it.
[LARPing (Live Action Role-Playing)] is a form of role-playing game where the participants physically act out their characters' actions. The players pursue goals within a fictional setting represented by the real world while interacting with each other in character.