Other possibilities? it makes sure that the neighbours all take Russia into account in their future plans. In the percieved monopolar world a lot of countries were ignoring russian feelings, if their actions could be seen as fine with the U.S. This could be seen as Russia reminding everyone its still in the game, without them having to do something directly threatening to any other major player. Any idiot can face a crisis - it's day to day living that wears you out.
Why recognise them ?
probably end up forced A vivid image of what should exist acts as a surrogate for reality. Pursuit of the image then prevents pursuit of the reality -- John K. Galbraith
I don't know.
The difference recognising these republics makes, is that they create a situation they cannot wiggle out of. This may be what they wanted. So you could be close.
But, aren't Turkish troops still in Cyprus, 30+ years after the invasion ?
Actually, I posted too fast, this reinforces your point.