Late landing clearances such as this one are quite common, especially at busy airfields. They are often heard at Heathrow for example. As noted in the video clip, if possible the controller might inform the pilots to expect a late landing clearance and the reason why in order that they don't do a go-around if not necessary. Typically the late clearance will be due to waiting for an aircraft or checker performing a runway inspection to vacate the runway.
Although I work in the En-route centre, on visits to various towers I've often heard the controller drag out their speech, such as slowly saying the surface wind before actually giving the landing clearance. This gives the pilots a heads-up that they will be cleared to land, again reducing the likelihood of initiating a go-around.
Although not common, it is not unusual for the wheels to touch the runway whilst undertaking a go-around.