Tower asked "are you going to continue" and they replied. That sounds like low speed (high speed you wouldn't reply that quickly, focus on takeoff first). And at low speed if it went through the engine you would abort the takeoff.
With most airlines the rule is "below 80kt stop for any warning or caution, above 80kt only abort for engine failure, fire, or unable to fly"
Also in Part 25, V2 cannot be less than Vr which cannot be less than V1. They call all be equal, but V2 cannot be less than V1 by definition.
Pilots will wait until at least Vr but not before making sure the airplane is tracking straight down the runway before lifting the nose wheel off the runway. At least that's how my airline teaches it...
That's a safety margin in the calculation, because you still need to move the thrustlevers and in some cases manually hit the brakes. Can't do that in a millisecond.
But that's all in the high speed regime. What I was commenting is that from the radio calls you can deduce that this bird did not go through the engine as claimed. They just hit the bird.