Does this require the replacement of the whole motherboard?

what ever that integrated chip was for (the numbers on it are burnt off so can't be looked up) it was there for a reason.
not only has that chip gone pear-shaped, and therefore whatever it controlled is also dead, but the reason why it went south also needs identifying otherwise any replacement part will suffer the same fate.

and, what else has been affected?
as by that picture, there are shorted out pins, melting caused by over-voltage and/or temperatures, and the IC next to it has been affected.
you would also need to flip the mobo over and see what is on the other side - as you may only be seeing the tip of the iceberg so to speak.

in short, it may be a $5 part and only require 1 hour labour, but getting a replacement IC and desoldering and resoldering without causing further damage, plus the likely hood on downstream issues, and not knowing the root cause would make me either cough up for a new board, or if the laptop was long in the tooth or wasn't servicing my needs, take the opportunity to get a new one.

wasn't under warranty, or covered by house insurance was it?