They certainly have a clarity to their movements. What is it that separates this dancing from other examples?
How would I go about beginning to learn to dance like this? I understand they are exceptional and it would take me forever, but it looks like it would be worth the effort.
(Or maybe it's my mood on a quiet Sunday morning when I haven't been dancing in almost a week.)
Well, they are Adrian and Amanda Costa, so if you live in France you might not have a problem. If you read French,
you can see a summary of what they see as important here, and you can look for a teacher who emphasises the same things, and whose performances (if any, and there won't necessarily be any) are consistent with that in as far as you can judge.
Here's a somewhat rough translation for those who don't read French.
Dance: Essentially, argentine tango is a social dance. To dance for the social dancefloor, is the pleasure of evolving together, and taking part in a whole in which everyone gives up some of his freedom to someone else.
Musicality: is the art of walking as a couple in harmony with the music. With their movement, the couple choose to reveal an instrument of the orchestra. "Dance is music made visible".
Posture: to feel our pressure against each other and towards the sky. To welcome the other person in opening one's torso, to go towards him, to feel the pleasure of elegance. [I'm having real problems translating this one, sorry - it doesn't sound at all odd in the original, but I haven't time to sort it out just now]
Embrace: to take the other person in our arms to unite and connect without losing onesself. The magic of the embrace is to see the fusion of two persons in one another's arms walking with the music.
Or, broadly speaking, you can look for a teacher who sees their mission as teaching 'salon' tango and only that, or sometimes 'social' tango and only that, and who puts a lot of emphasis on the music and the embrace.
As far as my experience goes, what teachers choose to say or not say about what they want to achieve is pretty trustworthy, at least in cases where they're saying something specific. Of course some who aspire to anything can deliver it more than others, but to the motivated student the important thing is that they're trying and that what they're trying to do is what you want.
The alternative, equally broadly speaking, is a range of more elaborate, technically focussed and physically demanding approaches that are fascinating in terms of technical possibilities and physically expressive dance for its own sake, but are probably not what you need to spend your time on if you liked that video a lot.