There are spells that sound "a lot older than Latin", and (at least in canon) there's a spell with incantation "point me" (Goblet of Fire, iirc).

I think that's Harry's point about Wingardium Leviosa. That it doesn't make sense for people many thousands of years earlier (as far back as Atlantis) to have created a spell that looks like a Latin-English mangling. That's why the immediately following sentence to the passage you quoted is:

Harry slumped over at the breakfast table, resting his forehead wearily on his right hand.

So basically he had made a hypothesis (preprogrammed program-instruction by the people of Atlantis), but his theory seemed to collapse on this bit, that the language didn't fit.