I believe you may have misunderstood/misheard the controller's explanation in the clip you linked to above.
"I need to have the first arrival off the runway and you rolling before the second arrival comes inside two miles final or I lose it....." (my transcription of most relevant controller statement)
Key difference being the controller needs the departing aircraft moving when the arrival is at two miles final (with expectation that the departure will be airborne by the time the arrival reaches the threshold) vs having the departure actually airborne when the arrival is at two miles final.
Hence, on your Monday experience, no need for go around as that departure was likely rolling before you were two miles final.
In any event, the two mile final is most likely a local practice/guideline/procedure, and is not a formal separation standard. My best understanding is there is no difference in standards canada/us on this point: no simultaneous runway occupancy (eg as mo32a quoted above). If they get the departure rolling when arrival is two miles back, then things work out, if not, then you get the go arounds the controller mentioned.