Looking at the inputs in TAStudio, it's pretty evident to me that this run was made with real time inputs, as the author was mashing the button on the main hub. The movement in the levels feel a bit more like there was rewind involved, and the tools available in BizHawk were not used. There's even a moment in the yellow switch room where Mario never starts running at maximum speed, which loses a significant amount of time, and makes me wonder if this was the case for other levels as well.
Below is a 320 frame improvement up to the save box to showcase how much faster this run can be: https://tasvideos.org/UserFiles/Info/638096931635039498
I don't have much to say about the category in question, since the amount of suboptimal movement here is a bigger concern. I would highly encourage the Author to learn some of the tools avaliable in bizhawk, the8bitbeast has some great tutorial videos that explain how to use the tools that I think will be really helpful. https://www.youtube.com/playlist?list=PLlJzD6wWmoXmihK13itZJ-mzjK3SD1EaM