To be a professional, you don't necessarily have to play the biggest tournaments.
There are millionaires who can play tournaments of 5k, and 10k without problems, but that does not mean that they are professionals, they are recreational players, who have the money to play such tournaments.
A professional may be someone who is playing poker full time, 8 hours a day, like a normal job, and poker earns an income to pay for living expenses.