The sounds of New Orleans rhythm and blues in the 1950s, as exemplified by the music of Fats Domino, was harmonically and melodically much like other regional styles of American roots music. Individually, the parts played by the different instruments could be traced to other stylistic sources, including Latin, country and blues. The rhythms, though, are unique to the sounds of New Orleans.
Many of Fats Domino's most popular uptempo tunes are played with a "two" feel. In this groove, the bass plays the chord's root on beat 1 of each bar and the fifth on beat 3. The drummer accents beats 2 and 4 with the snare drum (the backbeat). The result sounds a lot like country music, until you add a piano improvising around the chords, a guitar playing syncopated eigth-note figures against the bass and drums, and a horn section blowing harmonized riffs above it all. Each part is simple, but the whole is a complex, interlocking arrangement.
It's essential for a good rhythm guitar player to be aware of the role of each instrument on any given tune. The upper part of the drum set (the snare drum and/or cymbals) provides both a metronome and inspiration for inventing rhythmic guitar parts. The kick drum or bass pattern can be doubled to give the arrangement a beefier, low-end sound. Either hand of the piano can be augmented or replaced by guitar.
Ultimately, knowing the "right" part to play is a combination for listening, practice and experience, combined with a bit of on-the-spot creativity. This music is only "traditional" because it worked well enough to be worth imitating; once it was the cutting edge.
