Abstract art style employs lines and geometric shapes that are not meant to resemble anything in particular. Geometry Wars and Breakout are two well-known examples.
Early game developers often chose abstract visuals, because real objects could only be crudely translated into game graphics at the time; this was especially true prior to the release of the NES, on consoles such as the Atari 2600. Some games were given context in the manual or marketing that the game alone could not convey, such as Yars' Revenge or Raiders of the Lost Ark. Without this external context, both games would be considered graphically abstract. With it, however, they must be seen as heavily stylized or primitive.
'Abstract' does not simply mean stylized or cartoonish. Dictionary.com defines the word as it relates to art: "of or pertaining to the formal aspect of art, , etc., esp. with reference to their relationship to one another". For a work to be considered abstract, it should not represent anything real or derived from real life, even in a heavily stylized way. Thus the concept does not necessarily include games with exaggerated visuals like Guacamelee, visually minimal games like VVVVVV, and games that depict unreal creatures or worlds like The Neverhood.