My earlier answer was focused more towards academic libraries, which could be expected to be less enthusiastic about collecting video games, especially because of frequent shortage of funds for what are perceived as more "core" academic subjects.
For more focus on public libraries, try databases such as Masterfile (Ebscohost). Masterfile Premier gets 56 hits for the search (in full text): video games and public libraries and oppos*, and 42 hits for TX(video games AND public libraries AND censor*), for example.
You might also approach this from a psychological research perspective - TX (video games AND attention deficit) gets 8 hits in PsycInfo and 13 hits in PsycArticles, for example. Both of these commercial databases would be available at most large university libraries, and at some larger public libraries.