The point I think both of these anecdotes illustrate is that it's possible to be interested in gaming, and even to game a lot without being a "gamer."
"Gamer" is what sociologists and marketing experts refer to as a lifestyle. In this respect, it's similar to being a soccer mom or a goth or a sports fan. Alvin Toffler, the man who coined the phrase "lifestyle," believed that as post-industrial society became richer and more complex, it would begin to fragment. This fragmentation is due to the fact that our culture and economy is now too complex for anyone to understand all of it. There are too many humans with too many differences between them for all of us to fit into one gigantic '50s-style monoculture. Instead, humans have started to create subcultures. Thanks to the internet, you can now hang out online "socializing" with people you've never met and who don't even live on the same continent as you but probably have more in common with you than the guy living next door. BoingBoing's Cory Doctorow even wrote a book about the phenomenon called Eastern Standard Tribe, though I'd suggest that if you've reached the point where you're changing your sleep patterns to coincide with the peak activity hours of a chat room, the only subculture you're a member of is the mentally ill.
Having a lifestyle also makes it easier for people to market stuff to you. They can seek out subcultures and find the values that bind them together and tailor their advertising to fit the values of any lifestyle demographic. In fact, such advertising usually takes the form that you can express your identity and your membership of a certain subculture by buying certain products. For example, if you're a serious gamer, can you really live without a keyboard designed with first-person shooters in mind? Is your mouse mat really smooth enough? Do you have a bespoke case mod? Are you hardcore, or are you some kind of Wii-fondling casual gamer?
One of the most interesting instances of this phenomenon was the recent high-profile sacking of GameSpot's Jeff Gerstmann. A lot of digital ink has been spilled over this issue so I'll mention it only in passing but one factoid that the matter did bring to our attentions was a press release that revealed a change of staff at CNET, Gamespot's parent company:
"Stephen Colvin, former President and CEO of Dennis Publishing, the publisher of Maxim, Blender, Stuff, and The Week magazines, is joining the company as executive vice president. Colvin will be dedicated to overseeing the company's entertainment and lifestyle brands"
This means that the guy overseeing GameSpot is not a gaming industry insider, or a hardened, cigar-chomping, whisky-swilling game hack (possibly nicknamed "Scoop"), who jumped the fence from editorial to management but rather an expert in lifestyle magazines, one of the creators of Maxim.