The vast majority of tracker music was initially in a format called MOD, since it originated the format. MOD's specification was matched to the capabilities of the Amiga sound chip, which proved limiting as time went on, so other formats emerged. Formats and file extensions now include STM, S3M, XM, and countless more. The collective term "tracker music" is easier than trying to enumerate them all.
Trackers are differentiated from note-data formats like MIDI in that a tracker song includes the samples themselves, little snippets of WAV-like data which are played at sped-up or slowed-down sample rates according to the note data. Whereas a MIDI file only includes the notes and timing information, which gets sent to "instruments", which are responsible for translating those commands into sound. Different instruments may do it differently, so a MIDI can sound vastly different depending on what player you're using. A tracker song will sound roughly the same everywhere, barring bugs, with the only difference being that certain player software may have higher-quality math (higher CPU usage) for the sample-rate adjustment and mixing.
Because of their self-contained nature, containing only the sound samples actually used in a given song, tracked music was popular in video games and in the game cracking scene alike. (All the music in Star Control 2 is embedded MOD files, for instance.) And like anything else in what became the demo-scene, the mantra of doing more with less, making enjoyable music in just a few K of note data and samples combined, became its own factor to compete on.
Modarchive.org is the place to go to experience tracker music now; there are players that run in your browser. Click through the top couple songs and you'll get a feel for not just the format but also the era, since the heyday of MOD was the early 90s, much of it fits right into what we now nostalgically think of as 90s electronica.
But even with the original MOD format, Bjorn Lynne / Dr Awesome wrote a lot of Prog Rock MODs inspired by Genesis and other bands.
I think my favorite opposite-of-electronica would be Joegir Liljedahl's "Guitar Slinger", which he somehow manages to fit into a 4-track MOD, but it sounds like there's so much more going on.
Smallest-favorite would be "echoing", which is 43k uncompressed, and manages to be pretty listenable despite its simplicity. It's really fun to watch the rhythm track in a player that shows you the scrolling data...
Here's the first one I found
https://www.youtube.com/watch?v=i9MXYZh1jcs
He gets into the explanation of how the tracker software works about 8min 30seconds in.
Typically though if you got a cracked game at that time it would have the crackers group name and there would be a little graphical demo and some tracker music.
I think "Tracker" is the name for a service that keeps track of p2p links. Some trackers are/were extremely exclusive and tight-knit with interviews and quizes to get in. You also had to work hard to maintain an upload/download ratio. Some, like thepiratebay are open and simply highlight quality downloads.
What.CD was a legendary private tracker if you want to look further into it.
The article barely touches on this, saying vaguely "The songs that were stolen were often used in keygen cracking software that was popular in the 2000s to pirate software" -- so the music was used as a key for the keygen? Or was it just included for giggles? Or is it a fingerprint intended for actual tracking?
edit: thanks for all the replies, some really great info below!