Children do act up at that age, particularly at birthday parties, and the host and other parents know that. What matters more is how you deal with it to a certain extent. I've found the worst offenders are often older siblings!
However: When various games were played he was aggressive and not following the rules which having seen this at parties with that age it does put pressure on the hosts and make everyone else feel awkward. You don't actually say what you did at that point to help him to stop this.
What I would have done:
At the first instance sympathised that he hadn't got the prize he wanted, while pointing out that you don't always get what you want. Probably made a joke about putting only spiders in his pass the parcel for his party.
Then I'd have taken the catapillar off him, and got him to apologise to the host or the child with the spider depending on what seemed more appropriate.
On the first game he didn't follow the rules I would give him one warning, then pull him out of the game to sit with me. If he did it again on the second game then I would have left.
The thing is the talking nicely afterwards would have made little difference to my ds, who sounds quite similar. Unless we were going to another party very imminently (within a fortnight) he'd have forgotten about the threat made last time.
And the other parents would have seen me sitting there bleating "play nicely ds" and it not being effective.
Ds found parties very stressful at that age, due at least partually to glue ear so givne the amount of background noise, and he couldn't hear, so he only had a limited point before he got overwhelmed. So I used to give the hosts advanced warning of this, explaining that I would remove him if he got to that stage. I also used to sometimes find taking him outside for 5 minutes in the middle of a party could make a huge difference to his behaviour, so I'd explain that to the hosts too beforehand.
I did develop handsigns for ds to let him know how things were going. A flat hand held downwards means "you need to calm down"; a beckon means "you need to come outside" (which he was usually glad to do); thumbs up "doing great"; hand on mouth "quieten down"; and a point to the door means that if he doesn't stop immediately he's going home.
It worked well in that it gave him the opportunity to manage his behaviour without me speaking to him.
If he's usually fine though I would take it as a one off and not worry about it too much. I had to deal with it as ds would generally get ex and shoff during parties so it needed to be leant on fairly heavily.