If you look at the chart in the Popular Science article, you'll notice that while the "#gamer" tag is the nerdiest word on the chart, it is also in the top 5 geekiest words. Clearly, based on this data, gamers are both.
Personally, I find the geek/nerd divide to be largely irrelevant, primarily because everyone seems to a different idea of what the distinction between the two are. Given the lack of consensus regarding how to distinguish between the two, I prefer to treat them as synonyms.
I vote "geek". I like to think that most board gamers aren't completely socially inept.
Going off this Venn diagram:
Board Game Geek - pretty much everyone who frequents this site
Board Game Nerd - subset who frequent this site, not too social/talkative, hates luck, over analyzes the rules and strategies, corrects others, gets annoyed others play differently than they should, very uptight.
Board Game Dork - subset who are smelly gamers or eat messy/greasy/cheesy foods when playing.
I've always thought of it as something like nerds were someone who wanted to blend into society but couldn't. Geeks were people who weren't interested. I.e., nerd was a label which someone got as a result of other people's actions; geek was a label which someone gave themselves.
Part wants to say geek since that's what I classify myself as, but I've been to a few game auctions at local stores and it's overwhelmingly nerd. They were almost like poorly drawn caricatures of nerds from Saved by the Bell. I guess it matters on the reasons that people play. If it's social, thematically obsessive, etc. Point being, there are gradations of why people are here and as a consequence we can't just think in terms of absolutes. We are as diverse as the classifications themselves. All are probably applicable.
I like to think that most board gamers aren't completely socially inept.
If they had more social skills we wouldn't be drowning in low interaction games where prime design objective is to protect gamers against each other.
This video just came out yesterday, perfect timing for this discussion:
Dang, seems like I'm a geek between all the nerds. When hipsters came out I had 10 kg too much to fit in, but then I lost them. Now I fight the urge to grow a moustache as I'm just to hip to be like all the hipsters.
Only I'm usually smarter than the nerds.
From Dictionary.com: nerd-an intelligent but single-minded person obsessed with a nonsocial hobby or pursuit.
Geek-a person who has excessive enthusiasm for and some expertise about a specialized subject or activity.