Can I not get downloaded files from iTunes off my computer (Mac) and on another device (Windows) for DJ-ing?

The standard music player applications on Macs – Music on modern Macs, iTunes on ones running Catalina and earlier – like to store files inside of their own database. The idea s that you won't mess around inside there; that you'll use the use the user interface provided by the Music application or the iTunes application to play songs.

However, if you're talking about purchased music that has no DRM on it, it's very easy to copy it out.

Open Music or Tunes, select the songs or albums that you want, and drag and drop them from the application window to the Desktop or to a folder. This will make copes of the song files. Note that the copies will typically have filenames that reflect the name of the song, but not the name of the artist or album, so if you want to keep all of the songs from one artist or album together, you may need to do multiple small copy operations to multiple folders.

Note that if you are copying files onto a USB flash drive, the Mac finder may add metadata files such as ._SONG1.MP3, ._SONG2.M4A, etc. alongside the actual SONG1.MP3, SONG2.M4A, etc. These files can confuse non-Mac systems which get fooled by the extensions, think they are music files, and try to play them – only to discover that they are "corrupt."