While there's frequently overlap between the two, Otakus and Gamers are non-exclusive terms.
Otaku is more widely used to describe Anime fans. Though it could apply to hardcore gamers as well since being an Otaku just means near-obsession on something but it's more of a Japanese term otherwise.
Just saying, because Gamers have a somewhat negative reputation as it is, adding the infamy of some Anime fans/fandoms only multiplies it...
Bit of a tangent though, sorry 'bout that.