Honestly, as a native English speaker, I can't say "my guy" is used often, "boyfriend" seems the most obvious here.
"My guy" would only really be used if you're talking secretively about someone helping you. E.g. "I have a guy who can help me out... my guy will help" or whatever.
My guy, gets used between close friends. It's pretty informal and usually used by young people. People say "whatsup my guy" (it's like homie, bro, fam, buddy, or dude).
Only saying guy can seem rude especially if it's the first time talking to someone because it's sarcastic. For example during some kind of dispute people would say "Get out of the way guy!" or "Give me a break guy." It's like calling someone buddy when they are obviously not a friend. Double rudeness for calling a female "guy".
Sorry I don't mean to give a lesson on slang here I'm just wondering if it gets used like this in Russia.
Relying on the dictionary hints is more often than not bound to cause mistakes, because they are usually wrong, misleading, or incomplete. Besides, the appearance in the hints simply means that "guy" is a valid translation in some instances. Мой парень, however, appears to mean "my boyfriend". "My guy" is actually much broader than that - used, for instance, by mothers to refer to their baby sons.
I'd say it's not great. To me "partner" implies someone you're living with, someone you're in a long-term relationship with. "Boyfriend" could be that, but it could just be someone you're dating. Translating "парень" as "partner" isn't necessarily wrong in every context but it narrows the meaning somewhat so it seems less than ideal when there's basically a perfect match available.
Aargh. After just being told by Duolingo that "I has stood..." is correct, I am now told that "My guy" (cf. john.newbe's comment) is wrong and "My boy" is right even though the hints gave "guy" and not "boy." Although I might hope that my girlfriend would say of me , "He's my boy," she is not going to say "My boy ...." On the other hand, I would expect her to say "My guy ..." as well as "He's my guy."