I agree. One could say there is a upper level of gamer which would be the Hardcore gamer, who is usually the PC gaming type. The only reason to game on a PC imo is if you are going to be dropping money on a high end rig to play games at a much higher quality than consoles can offer. And if you are into it, being able to Mod games.
But a gamer is a gamer no matter their platform choice. If it something they do very frequently, then they are a gamer.
But the thousands upon thousands of hours a year I invest into gaming on Consoles still qualifies me as a gamer, whether I have a PC or not.