I know this is an old question, but I believe it is because if the (-OH2)+ group left it would reform the carbocation. Carbocations are pretty unstable compared to the (-OH2)+ which gets deprotonated really quickly into the stable -OH group.

2:28 He said there's a proton transfer, so I assume it's just like any other video (where the lone pair in other H2O attack the proton in the H2O+ part of final product and cause the H to pop out and leave behind the final product). He just writes is as -H+ instead of writing the whole proton transfer mechanism.

Think about it...after deprotonation oh the H2O, to further stabilise the molecule of oxygen, the product became an OH attached to an R group (so an alcohol/hydroxyl group). A hydroxyl group is not a good leaving group, as it is a weak base, and to have a strong leaving group it must be a strong base. If it leaves, it will have a formal negative charge, hence becoming an unstable hydroxide anion.

i also have the same question that if we were not given the final product then we would make a six membered ring.