Any gambler who has long experience, is in control, and is not easily swayed by emotion can be called a professional gambler. I believe this does not limit a person to skill-based gambling.
I doubt this alone would be enough to call someone a professional gambler, due to the fact that topics about professional gamblers have been popping up recently I had to check what the definition of a professional gambler was and according to them, a professional gambler shouldn’t just be able to control their emotions but should also make gambling one of their means of living, they should take it as a job and not some fun activity.
If were to so consider the few characteristics that you listed it means that a long time gambler who only comes to gamble for fun would fit into the category of a professional gambler because most people who take gambling for fun usually have good control over their emotions and have experience (depending on when they started gambling). And I don’t think that’s entirely true.