That was milonga, one of the three primary sub-dances of tango, though the technique overlaps almost entirely. Here is the most common style, actually called tango (words are heavily overloaded in tango): https://www.youtube.com/watch?v=KiT4OS6MKVQ

For completeness, here is the 3rd main type: https://www.youtube.com/watch?v=oWSugQxwpEA

Worth mentioning it is entirely improvised.