In it's broadest sense, the term for this kind of repetitive accompaniment is ostinato: a repeated bass figure over which a melody occurs. Ostinato, however, can refer to a whole repeated sequence of notes or chords; it need not be a single chord.
Stylistically, the songs you're asking about have their roots in traditional New Orleans jazz. For example, listen to the guitar and drums in this recording. It's often called "four on the floor", which is a reference to a kick drum (bass drum) being played on all four beats of a measure, or more generally to the rhythm section as a whole.
Doctor John often uses this style, or variations on it, as does Randy Newman.
But short, repeated chords on each beat can show up in other styles. For example, Bohemian Rhapsody, "I see a little silhouette of a man...", owes more to classical music than jazz.