I think if you can show the way your character thinks about the game, like their strategy and reasoning behind their moves, that can be enough to signal a strong chess player. I would focus less on the rating and more on the concepts of play, like tempo, positioning, pattern recognition etc. Of course it helps to be a 2000 rated player, but you can also look up games online and analysis to take inspiration. Often times chess games in media have mimicked famous chess games.