It's not Chinese-influenced design (which rules out much of Asia) - there's too many even numbers of steps, pillars etc. I think the hat on the man at the bottom right of your linked picture has a hat that I think is referencing Song Dynasty hats? (Ming Dynasty maybe?) In Amok Time, it looked to me like they were using very ancient things rather than elaborate, which makes sense for that particular ritual, I think!

The giant statues that I've seen personally have all been Buddha, but there's so much variation just there. Even Buddha sometimes has a sword, though it's said to be to banish ignorance rather than be used as a weapon, but I don't know how much of that is later interpretation!