You're already calling me crazy. Hold on a minute. (or skip to the TLDR version at the bottom~)
 
This is history as I'm seeing it: 

I'm looking at this as a matter of definition. For a long time all games were in the realm of the tabletop, and "role playing games" made sense in comparison to classic abstract games (Board games and sports very rarely have a profound back story to them). Even wargames, which model real world combat, were often isolated conflicts forever being told and retold with no consequence on each other. But with RPG's, Instead of being the general on an ethereal checkerboard battlefield, players were jumping into the "role" of an individual with an entire plot ahead of them. A new term for a new game experience.  

For a time this went on, and all was good. Until video games.  

The impact wasn't immediate. During the arcade era, video games were created in a similar mindset to classical tabletop games. For a time, hardware limitations forced a sense of abstraction to game elements. Slowly games gained more resolution, and developers were able to add more definition to their games. Triangles became ships, gained colors, and so on.  
Some people might point to this time period and half sarcastically say "Well, in defender you play the 'role' of a space ship pilot. So doesn't that make it a role playing game?" Logically, that could be a sound argument. The loss of abstraction also seems to fall on the RPG side of the definition from the tabletop era. But even as hardware increased and games gained setting and themes and back story, games remained these isolated experiences. This was still a stark difference from RPG's. You start a game, you play until you die, and then that game is wrapped up and tossed into the void of the infinite. You could start a new game, as long as you had more quarters, of course.   

That was the importance of the home market. Even though the mindset stuck for a long time that games should be short and repeatable, eventually designers began to understand that game experiences could be longer and have more permanence. Passwords came about, and are a kind of remarkable invention in this context. But the point is that games were developing from short isolated events into longer experiences which had room for not just clearly defined characters, but even character development and plots with twists and other such elements of storytelling.  

Fast forward to current day. The possibility for narrative is being well explored from many fronts. Traditional storytelling is exercised in games, linear plots and narratives are alternated with gameplay that challenges the player. Designers are also delving into ideas of immersion and social aspects among other areas. Most importantly to RPG's, the idea of player agency in storytelling is a topic which some developers are focusing almost their entire efforts on. Bioware's Mass Effect and Dragon Age games are probably the most spoken of games in this area, and with good cause. They give the player character to fall into the role of, and they they allow that player to develop their interpretation of that character given the world they are in. They are as close to the pure RPG experiences offered in the pen and paper days.
 
Now the actual argument I'm trying to make here: 
 
Bioware games are close to pure RPG experiences, but they aren't. Pen and paper RPG systems were created to facilitate storytelling and, well, role playing. The characters, and the players acting as the characters was the core that the games were based on, and the systems built around that. Video games have a number of existing cores, however, looking at existing VG genres. Platformers, FPS, RTS, action / adventure... the list can be pretty long, and at times very vague. I don't know if RPG should even go on that list. 
 
Personally, I don't think it belongs there. Not when a popular decision for designers is to slap some "RPG elements" onto whatever game they happen to be making. If RPG's can be distilled into a syrup that you can pour over whatever genre that you want, then it can't be a genre on it's own, right? 
 
Looking at it backwards, even the games I mentioned could be consider to be of other genre's with RPG mechanics. Mass Effect is a third person squad based shooter with some cover mechanics and special skills. Fallout 3 is basically a sandbox first person shooter. Castlevania SotN is an open world side-scrolling platformer. Are they RPG at their core, or are they defined otherwise with RPG elements? Can RPG's even exist in video game form, or is there something about the tabletop realm that defines what an RPG really is?
 
Or is there something else at fault here? Are video game genre's laughably vague and murky so that they are beyond use? Is "RPG elements" a misnomer for what mechanics like leveling up, side quests, and loot are? Am I just a crazy person? 
 
All of these possibilities seem equally likely to me, so I ask the public. Do the people see any truth in this argument?
 
PS. For sake of argument I'm ignoring JRPG's and MMORPG's. MMORPGS's are more about social aspects, avatars, and slaying/fetch quests then they are about telling the stories of the player characters. JRPG's, regardless of their story writing and telling, are often terrible in terms of gameplay and player agency. I'm going to write an article later about why they're bad games as well as bad RPG's, so please yell at me later for that.) 
 
TLDR version: 
 
RPG elements can be applied to anything, and all of today's RPG's could be defined by their other systems (FPS, platformer, etc). Are there actually any RPG's anymore?