Personally speaking, I am hesitant to categorize dinosaurs- even within the framework of causing mayhem in current day- as giant monsters. The very definition of the word ‘monster’ refers to something that is unnatural or abhorrent; dinosaurs, while definitely strange in appearance, are still members of a once naturally-occurring animal species. An elephant is a large and odd-looking creature too, but I would similarly never classify a movie about a rampaging elephant as a giant monster film (that is, unless it was an undead, alien-possessed elephant).
This seems like an odd position for me to take considering that a little while back I committed a post to the Dinosaurs Attack! Trading cards; but as said dinosaurs were mostly portrayed with zero scientific correctness and fantastical exaggeration, it gets around my “animals verses monsters” stipulation. Understandably, most portrayals of dinosaurs in film outside of documentaries are often inaccurate to some minor degree, but I’m referring here to wild, science-defying embellishment that treads into the realm of the fantastic.
This also extends to fabricated dinosaurs like the Rhedosaurus from The Beast from 20,000 Fathoms. Even though the creature is supposed to be a member of a “real” species in the film’s story, the Rhedosaurus is clearly an imaginative creation despite its context.
I suppose that the bottom line here is that (for me, anyway) giant monster concepts need some sort of fantasy/sci-fi component in order to properly qualify as such. Dinosaurs are ultimately too grounded in reality to count, but that’s just my own little opinion.