Reddit mentions of Beyond Salsa Piano: The Cuban Timba Piano Revolution: Vol. 1: Beginning - The Roots of the Piano Tumbao

Afro-Cuban music is built largely around interlocking rhythmic patterns, so a large part of it is learning how these work so you can function within them rhythmically.

The biggest important concept is that the rhythmic patterns revolve around the clave, which is a 5 note figure that dictates the rhythmic feeling (one half relatively straight, the other half more syncopated). The two sides are interchangeable, so you have to know which pattern a particular song is in or you'll play the rhythms "crossed", which in this style of music is the rhythmic equivalent of playing in the wrong key.

The basic rhythm of the clave is usually divided into 2 measures, one with 2 notes and one with 3. We refer to the two variants as 3-2 or 2-3 depending on which measure starts the phrase.

2-3 Clave
|------|-----|

3-2 Clave
|-----|------|

In the example you gave here, the opening riff is actually clave neutral (i.e. playing the same rhythm on both sides of the clave), but the other rhythms in the song indicate that it's in 2-3 clave. This example is also in 2-3 clave, but the opening riff follows the clave:

Clave
|------|-----|

Opening riff
|-*--|----*|

Notice that the 2 side of the riff is the only one that plays on any beats (1 and 2) and from there it goes off on to a string of offbeats. Generally, the 2 side of the clave has a straighter feel, and it's especially common for rhythms on the 2 side to line up on beat 2. You can read more about the clave from one of my old posts here.

If you can read music, I would suggest looking into this book as it explores how these riffs evolved over time. It's written from a pianist's perspective, but all the examples are transcribed from string instruments.

Speaking of instruments, the other important thing to get this kind of sound is to have doubled strings. Cuban music often uses an instrument called a Tres, which is essentially a small scale guitar with the strings arranged in 3 doubled courses instead of 6 strings. If you're handy with tools, I've had some fairly good success simply getting a cheap 3/4 sized guitar (or smaller would probably work better) and recutting the nut and saddle. La Bella makes easily available strings.

A Laud is sometimes also used, and Puerto Ricans (whose traditional music is very similar to Cuba's) will commonly use a Cuatro.

Here is a nice example of the Tres being used in a more modern Afro-Cuban context.

There's usually also a traditional guitar strumming chords, but I assume you want to get a bit deeper into how the music works. Let me know if you have any other questions!