From what I've observed, some people (emphasis on 'some') equated the no-delay abilities in popular games like World of Warcraft - the icons that let you keep clicking them with no cooldown. Of course, on closer inspection the analogy leaks like a bullet-ridden bucket. "At-will" abilities in video games are typically linked to a mana pool, limiting how much they can actually be clicked within a time period before having to wait a bit. This is ironic, given that the chief complaints from at-will opponents concern 'infinite resources'.
Another important difference is that in D&D, the at-will spell caster has to wait till everyone else has had their turn before casting another at-will. Contrary to rumour, it's not "PEW-PEW', it's "PEW-wait-PEW". I've never heard of a video game which operates like this. Video game abilities with a delay/cooldown on them are about the closest you can get, but those are usually tied to mana pools as well.
So I think at-will magic has become related to video games because a) those have a bigger mindshare compared to books than they did 10-20 years ago, and b) a few folks noticed a superficial similarity between icons that let you keep clicking & at-will spells, yelled very loudly, and the comparison stuck.