The punishments that you are referring to are all normal under Article 15, non-judicial punishment.
So, while it certainly seems an unusual pattern of punishment, it is actually exceedingly common in the military, for better or worse. These punishments could only have come from misconduct that occurred as a result of the alcohol abuse, because just merely being intoxicated is not enough to legally justify any of these punishments.
The only recourse for non-judicial punishment is an appeal to the next level commander. I know this seems rather like there are no rights, but that's because of the forum of an Article 15. Soldiers do not have to accept that forum. They can legally request a court martial, where they would have the rules of evidence, criminal procedure, legal representation, appeal rights, the right to be heard by a jury, etc. When a soldier accepts an Article 15, they give up all of those rights.
Now, there is no way he can get an dishonorable discharge without a full court martial, so that was an empty threat by what we've already determined was an unprofessional commander. It doesn't really change what the last bit of advice was concerning this commander. All he can do is report the behavior, which is not illegal but very unprofessional, to the IG.