In any kind of music with regular beats, the most important factor for a performance to be perceived to be 'keeping time', is the performer's ability to play in time to their own internal sense of time, and the ability of all of the musicians within any ensemble to be able to synchronize their internal metronomes with each other.
Some styles of music, for example, boogie-woogie piano are clearly driven by the left hand patterns, but the performance is still guided by the performer's own internal sense of time. A listener, or even the performer, will perceive the left hand to be 'keeping time'.
It is possible to play a melody on the piano, unaccompanied, with either hand and still be perceived as 'keeping time'.