While I have little experience with live extracts, I suspect the main effect of mechanical agitation is to change the consistency of the mixture. A complex mixture of related organic compounds like this will have all sorts of possible states depending on the exact mix of which compounds. Some are liquid at room temp, some are solid, and many will mix/dissolve in the others. The smallest change of temperature and/or the constituents will change it's appearance and state between liquid and solid.
The stirring is a wet lab technique to promote crystallisation of one (or more) compounds mixed/dissolved in others, and this will change it's state.
If one primary component of the mix starts to crystallise out that may release another compound from the matrix of mixed substances, allowing it to pool as a separated liquid ("the terpenes coming out").
I may be wrong, but it certainly appears very much the same process. It's purely a physical state, not a change of chemistry, and it's not drying it out as such (although roughening the surface will slightly increase evaporation of the more volatile compounds), there's no water or other liquid vanishing magically from it.
It won't 'repair' a degraded sample by undoing chemical breakdown, but it may present an nicer experience if it allows terpenes etc to be more appreciated by allowing them to be released more effectively, but I couldn't say on that side.
