H-C-C(+)-O-Mg(-)Br2 → H(+) + C=C-O-Mg(-)Br2 → C=C-OH + MgBr2 → H-C-C=O + MgBr2
Is it more clear, now?
What was missing before, is that oxygen is a Bronsted (Lewis) base and MgBr2 is a Bronsted (Lewis) acid and thus, a negative charge must be drawn on the Mg atom of the -O-MgBr2 adduct. There is no leaving of a bromide from MgBr2.
-O- + MgBr2 → =O(+)-Mg(-)Br2