Tournaments run with a time limit. After the time limit, the game ends in a set number of turns. There are also rules for "slow play" that generally keep a single turn from lasting too long—and inadvertently prevent certain weird combinations of cards from working.

Online play has what is effectively a chess clock. This doesn't work in person because the game involves "priority" passing between players after every single action, which would be difficult to do manually. Additionally, play in person relies on a whole bunch of "shortcuts" that skip steps if both players don't want to do anything, which would make timekeeping even more difficult.

But if you left out these tournament-specific rules and just played the game rules, you could have games going on arbitrarily long. Since you can create "tokens" you can have arbitrary amounts of state, so a game could even loop without ever hitting the same game state twice. (Think "puffer trains" from the John Conway's Game of Life.)

If there is a truly unstoppable loop (considering usage of the word "may" or such optional ability to continue or break a loop) then the game is considered a tie. There are tournament rules regarding players intentionally drawing out the game (it's against the rules), but I don't think there's any rule against a deck that simply runs long (or really long).