I thought the same at first, but then I tried actually saying it out loud. "Yeah, I'm just gonna go to the shops". And I actually think Munroe has it right here, at least for my accent. If I had been asked to say it and carefully analyse it myself, I probably wouldn't have noticed at all that I was eliding more than "going to" to "gonna". And if I had noticed, I still probably would have analysed it as (and I'm using Hangul here because frankly I don't know how to spell out the vowel in the Latin alphabet in a way that actually makes sense) 근 (basically "gun", but with a lazier vowel). But it's definitely been elided down to a single syllable.
The key thing is that this only happens when putting it into the middle of a full sentence. If it's the only word I say, it stays "gonna".
edit: wait 🤦♂️. I can use IPA. I'd have analysed it as /gən/ But realistically, Munroe's /gә̃/ is probably more accurate.