In music history, 3/4 (the waltz) was called "perfect time." 4/4 time was called, and still is called, "common time." At the start of a piece a "C" is written for "common time," and is still often used to denote 4/4 time by today's composers. The word "Common" is used in this sense as "less than perfect" or "vulgar" (in the Latin meaning of that word). The theology of the Trinity and the huge influence of three on Christianity out of Stoicism influenced this idea of "perfect time." Is it really "perfect"? Absolutely!
So let's indulge in the myth of "perfect time." Vals is the perfect time in which to dance. Musically speaking we have some interesting things that can be done with the tango vals (waltz), and this video clip is a great example.
Gavito clearly thinks in larger phrases, the smallest of which is 12 beats long (4 measures of 3/4). The common dancer dances on ONE(2,3), FOUR(5,6), SEVEN (8,9) TEN (11,12), which is the downbeat of each 3/4 phrase. Since Gavito knows where these are, it does not confuse him to dance on every second beat of the 12-beat phrase (2, 4, 6, 8, 10 and 12), or the second beat of the normal downbeat (2, 5, 8, and 11), for example, which he does at the outset of the video clip. His partner and any woman with a few tango courses could follow him on this because he is exactly on these beats and they make sense. His steps on the first half of this clip are mostly on 2, 4, 6, 8, 10 and 12 of the 12-beat phrase. Then he comes home to the power of the downbeat and resolves with intense pauses.
Gavito is by no means the only great dancer who uses 2, 4, 6, 8, 10 and 12 or 1, 3, 5, 7, 9 and 11 in a vals. When one is dancing on these beats, it is as if one is dancing a waltz within a waltz (instead of 1 against 3 -- the normal waltz -- one is dancing 3 steps (a waltz) per 6 beats. Note: You will need to clap out 1, 3, 5, 7, 9, 11 (3 against 6 on the downbeat) or 2, 4, 6, 8 10, 12 (3 against 6 on the upbeat) while counting to 12 (over and over) to understand what he is doing. Watch first, stop the clip, and work out the rhythm with hand clapping. Then watch it again, and you will begin to understand his genius. [If you are a musician, the feel is quarter note triplets here.]
Gavito may not have known what he was doing. I discovered these things from feeling and then tried to figure out why they worked.
Have fun, and if you have questions leave a comment or email me at firstname.lastname@example.org.