These files are not public domain
Read it carefully, it only says “public domain musical compositions in a MIDI (Musical Instrument Digital Interface) file format.”
The compositions are public domain, the MIDI files aren’t - they are a derivative work (a translation) covered by their own copyright. Specifically, “© Copyright 2001 University of Arizona. All rights reserved” right next to a big “Contact us” link. Literary and artistic works that are derived (legally) from existing works have independent copyright even if the original no longer does. Mozart, for example, did not write his compositions in MIDI format.
Now, it may be the intention of the University of Arizona that you can use it but, if so, they have not made this clear. It’s possible that the authors (mistakenly) thought that because the originals were public domain, their derivatives would be too. The music school should have talked to someone from the law school.
All of the purposes that they talk about on the “Purpose” page are equally applicable to widely licensed (e.g. everyone) or narrowly controlled (e.g. staff of the University).
Overall, a prudent person would assume that these works are copyright of the University of Arizona and can’t be used without permission or a fair use exemption. Your proposed usage is not fair use.
However, there is a big “Contact us” link on every page so you can always ask for permission.