There are three primary models:
Circulation of games, where the patrons check out games and play them at home.
Game-based Events, where the patrons play games at a specific time in the library
At-Will Gaming, where patrons can play games whenever they want. These might be games that are always available (Chess boards or PC games) or games that are checked out for in-library use (console games for in-house consoles).
The fourth model might be the library fostering the creation of games through game design workshops or hosting design clubs.
Should a library have special times for gaming events or an area where games are always available?
It depends upon the goal of the gaming. If the goal is to build community, then the events work well for this as it brings people together. If the goal is a learning or literacy goal, then the games might be always available. Determine the reason for the games first and then make decisions from there.