How does a 'quasi-tenured' hire work in practice?
I don't see how this is really different from hiring somebody with a very short (i.e. one year) tenure clock.  The difference probably has more to do with the hiring institution's internal rules than anything else.

We had a senior hire with a one year clock a while back.  It wasn't labeled as "quasi-tenure," but that was basically how it worked.  You don't give somebody a one year clock unless you are overwhelmingly sure that the person is going to get tenure.  And that seems to be what this position is offering; the hire will start without tenure, but the expectation is that they will be fully tenured in short order.