Amex can’t see into what the charge breakdown is. Just make sure you hit the $300 and you’ll be fine.
Typically this is correct, and in this case, yes, an extra charge on the room for breakfast, minibar, whatever, would count. There are a lot of offers that, say, technically exclude gift cards, but that spend still counts.
That said, I'd look for data with Amex and Marriott. Given their close partnership with the cards, etc., it is possible Marriott shares the third-level data with Amex, and can actually tell and filter the spend per the terms. YMMV, I guess.
If there is a way to spend just a bit more on the room - +$10 for refundable vs. non-refundable, or high-floor vs, whatever, I might go through with that. I wish I could help. I'm checking into a Sheraton tonight and using this offer, but it's >$300. Sheraton YYZ is always over >$300 US, so I usually do a different airport hotel, but with this offer, plus the convenience, it's well worth it for this time.