I'm not sure if it's just that I don't know what the joke is in the first place, or if it's just one that doesn't work in my dialect so I can't parse what it's supposed to be 🤔
Ah, in the dialect I'm most frequently exposed to (General American, at least to whatever extent that can be considered a single dialect anyway) there's typically no blending of the syllables in "giraffe", so using it as a play on "draft" doesn't really come across clearly (at least without additional surrounding context to make the intended wordplay clear), but thinking about it I could see it making more sense if I picture it being said by someone with more of a Mid-Atlantic dialect (and presumably others, but that's a big one around where I live so it's the one I can imagine the easiest out of the relevant English dialects), since I think someone with a heavy Philly accent would probably blend it more into a single syllable
huh i speak General American (California) and most people here reduce giraffe to one syllable that sounds like jraff
Further evidence that General American is basically useless as a classification beyond just going "[gestures vaguely at the US and Canada]" 
what general region are you in? maybe it's only a west coast thing
East coast (specifically NJ), which probably factors into it, though I should note that thinking about it more I do know other people from the same broad part of the US (e.g. NJ, NY, PA, MD) who have thicker accents without necessarily getting into a full-on Mid-Atlantic or Metropolitan New York accent who would blend giraffe into, like, 1.5 syllables? Heck, actually saying it aloud, I think it's more accurate to say that even I blend the syllables a tiny bit (as opposed to keeping them two wholly distinct syllables), just not enough that my first instinct is to read it as sounding like "draft" 🤔 🤔 🤔