Game genres shift and slide around, are stolen from niche cultures when they become popular (see how collars came from meaning something specific to a specific subcommunity, to being a relatively mainstream fashion item divorced from that meaning; compare to how roguelikes came from meaning something specific to a specific subcommunity (http://www.roguebasin.com/index.php/Berlin_Interpretation), to being a relatively mainstream videogame genre divorced from that meaning), and along with that lose their specific meanings in favour of something more broadly applicable.
Arguments about what something means are missing the point that everything means something different to everyone, and this is smeared not only across cultures and peoples but also across time. Encountering a first-person game today is different from encountering one ten years ago.