I think a real player is someone that fully dedicates themselves to getting better and to understanding the game.
I see a lot of league players who, just upon watching them play or speaking to them, you can tell only play pool as a hobby or as something to just "do."
However, I've met a few people who I would consider real players (some are SL 5s, others are SL 7s) because you can tell they are immersed in the game. I don't think you have to be a master of the table to be a real player - but if you aspire to be one someday and are willing to put in the time to be one then I consider them a real player.
If we are talking real players based on technical skill then I'd say it's in the way they shoot: steady rhythm, fearless shooter, strategic thinker, and can handle problems and clusters, or move through a rack pretty seamlessly. Most league players don't exhibit those qualities, but I think real players do noticeably exhibit these qualities.
-Richard