The clue is in the name - "club player" - somebody who plays chess for a chess club. I'm a member of 2 chess clubs in 2 different countries. I'm a club player as are most, if not all, the players I know. Although I recognize a few players on the congress circuit who don't play club chess and whom I wouldn't regard as club players. The lowest rated is about elo 2000.
In the smaller of the two clubs I play for, where we have 4 teams, the lowest graded player who plays bottom board for the bottom team has a grading which equates to an elo of about 1250 and board 1 on the first team has an elo of just over 2200.
The other is a much bigger club with something in the region of 15 teams. The top team has 2 GMs playing for it, round about the 2400 mark, and the weakest team starts somewhere round about the 1500 mark.
None of the players in either of my two clubs makes a living solely from playing chess. Rather several of them earn some money from coaching. In club 2 one of the GMs, an IM and a couple of players round about the 2100-2200 mark earn some money coaching. In club 1 one of the players rated about the 1950 mark coaches.
I also don't think you can limit the definition according to whether or not a player plays international chess. In club 2 I know of one player rated about 1950 who has played in the last 2 world championships for 65+. He is in his mid 80's. Good luck to him. He should continue enjoying his chess as long as he can, but at the end of the day he is a club player.
So, I don't think you can define a club player by his rating, whether he makes money from chess or whether he plays in international championships. There is enormous overlap. At the end of the day a club player is somebody who plays chess for a chess club.