Ed T,

"Enjoy Yourself" would be labeled by most as ska, the predominant rhythm variety of 1963-65. However, one can distinguish this form of early ska, which is little more than Jamaican musicians' interpretation of boogie-woogie, from more unique ska grove that came to prominence in 1964, when drummer Lloyd Knibb innovated a new beat. I call the former "ska-shuffle, and it was a main style from '62-'63. The latter style came in in late '63, with tracks like this:

"Artie Bella"
It's still a type of jazz, as all the musicians were active jazz players though they'd developed new Jamaica-specific rhythms. The drum set playing is very syncopated and absolutely thrilling. And during the ska revival as "two tone" in UK, you really didn't hear groups that could manage that. What they (two played) really was indeed more akin to polka, and gave birth to the very plain rhythm that I think international audiences associate with "ska" today.

The Jamaican popular music industry began in earnest with local musicians replicating or adapting the predominately African-American popular music styles, jazz and r&b (in various shades), so yes, the impact is there in most of it.