How to practice without a partner (for leaders)
The dancer in this video certainly has a novel dance partner! But it's not just a 'party trick'. I once knew a dancer who practiced his tango for many hours with two sticks in the absence of, and as a supplement to, a female practice partner.
Practicing one's walk can be done solo, and in fact it's very useful to practice walking on your own, as well as with a partner. But a leader also needs to develop a very good understanding of the geometry of the follower's moves in relation to his own. The broomsticks can help with this.
There are limitations with this practice - the obvious one being that, unlike a piece of wood, a tango dancer's upper and lower body frequently twists and disassociates. This can't be replicated by a piece of wood that only moves as one block!
However, if a leader lacks a practice partner to work on this, teaming up with a pair of broom sticks is definitely better than nothing!