For the record, I believe InterContinental Hotels (Crowne Plaza, InterContinental, Holiday Inn, and other brands) was the first hotel group to announce the elimination of the tiny plastic bottles. That was at the end of July 2019.
https://www.cnn.com/2019/07/30/business/intercontinental-hotels-plastic-toiletries-trnd/index.html
I'd bet that these business decisions have been studied independently at each major hotel group. As such, I don't think any of them is suddenly doing this simply because a competitor did it first. But, if Marriott is following anyone, it's InterContinental and not Disney.