Yes he still needs a nap.
I give you a high-five for instilling this... because his own parents won't and don't want to deal with it.
Anyway, at 2 years old, they DO get like this and with tweaks in their naps/sleep times.
Both my kids did that.
I simply KEPT to the daily nap routines. And grinned and beared it... but did not relent. I DID have nap time. And they knew I would not give in to their occasional protests. And then it passes.
If he will nap on the floor, then so be it.
Both my kids, at THAT age, when through a phase, where they wanted to nap on the floor too. So that's fine. They got sleep that way. Then, I made it clear, it was only for now... not always. Then one blue moon, they did again sleep/nap in their beds. With no rhyme or reason. Just a phase.
You need to discipline him for wrecking your room and for kicking everything off your dresser. MAKE him pick it up and APOLOGIZE to you etc.
He was/is, probably over-tired. Over-tired kids, get unreasonable and fussy and willful.
But do not allow him, to destroy things.... you are his Grandma... he must show respect. Do what you think is best to correct him on that....
ALSO, for a toddler boy... make SURE he gets LOTS of runaround activity in the MORNING... boys need that, to expend their energy & tired them out. Then, PRIOR to actual nap time, make everything QUIET and calm.... allow him to "un-wind" and wind-down first... while verbally "cuing" him that nap time is coming up... so to get ready. Then, so be it, let him watch a CALM tv show if you must. My son likes "Little Bear" for example.
For my kids as they got older, they needed at least 1/2 hour to wind-down PRIOR to their actual nap or bedtime. To key them down. That is important to do, BEFORE actual nap time.
ALSO make it clear to him, that in YOUR house, he NAPS. Say "That is the rule...."
all the best,
Susan