It's not clear at all what he did or did not say to support. He has conveniently skirted around telling us that exactly. If he made even the slightest inkling that he wanted to stop playing, and expressed that even a little bit to the support team, then yes, they are 100% bound to do just that. And there are no exceptions to that. At all. Especially companies like partypoker that are legislated in EU and UK - they have very specific responsible gaming rules that they must follow or face severe consequences if they do not.
It's kind of like you never say "Bomb" in an airport. You don't even casually mention that you do not want to play or to close your account, or that you might be tilted or have a problem with a poker site's support. And if you can't stop yourself from doing that...well, in my opinion the break is probably a good thing.
That is all very true. If you feel frustrated after losing, then support is not the place to went that frustration. There is a sub forum here for instance, where you can do just that. Support is not there to listen to vents, they are there to take actions. And the only action, they can take in this case, is to close your account. So if that is not, what you want, then dont waste the time of support staff.
As for weather the decision made by PartyPoker was reasonable, we will never know, because as you say, OP has not shared the email, he send to them. It might have been a reasonable decision, but the communication was laughably poor. It took them four attempts, before they finally wrote something, which made sense and related to the situation:
"We have taken the decision to exclude your account based on the communication you`ve had with us.
Your account status will remain as closed based on a company decision, which we have the right to take as per our terms and conditions."
As for the rules, a company like PartyPoker has to follow in various countries, I dont know their exact wording. It seem reasonable, that they are obliged to take action, if someone express concerns about their gambling. But it also seem reasonable, that they are allowed to engage in some communication and verify, what the customer wants, before they close his account. It hardly breaks any rules to reply something like this:
"Dear XXX
I understand, that you had a bad experience using our services. Please let me inform you, that you can set deposit limits to regulate the amount of money, you are able to deposit with us per week or per month. You can also take a cool down period or request self exclusion for a period of 6 month. Please let me know, if you would like me to initiate a cool down period, or if you would like to self exclude from our services."
So yes OP has fault in this, and cooling down is probably not a bad idea for him. But I have to maintain, that PartyPoker also handled this extremely poorly. If PartyPoker had handled this professionally, I can not imagine, that a thread like this would have happened.
If someone from PartyPoker is reading this, they should learn from it and do things better the next time. And players should also learn to not contact support in a situation like this, unless they actually want their account to be closed.