[maxsilver]

> Are there any MtG tournaments which are played for real-money prizes ?

Yes, routinely. https://magic.wizards.com/en/articles/mythic-invitational although the prize money amounts can vary wildly, most are nowhere near that high.

> This seems to me to be similar to poker, and considered a game of luck

It's like half-luck, half-skill. Deck construction is largely skill-based (both directly and metatextually), but decks are randomized during shuffling, which is obviously luck-based.