For me there are 2 classes of orgasms: ejaculatory and non-ejaculatory. Ejaculatory orgasms are qualified by the accompanying ejaculation of semen that occurs, and a refractory period usually follows (except perhaps in ruined orgasms, but I am not well-versed in that). Non-ejaculatory orgasms do not involve ejaculation of semen, but CAN involve leaking of precum, and they don't induce a refractory period.
I think dry orgasm is just another word for non-ejaculatory orgasm (it isn't in the glossary).
It sounds like you are having non-ejaculatory orgasms. You, like many others, get accompanying precum. Awesome. Up to you if you want to apply the unofficial term "dry orgasm" to what you are experiencing. Otherwise, just call it an orgasm and revel in the sensations 🙂
Technically it's not a dry-O seeing as youre wet...LOL
But in terms of a prostate play as long as you arent ejaculating it can be deemed a dry-O