It wasn't lean in comparison to other MP3 players at the time. This is the thing I think people are forgetting. It was in comparison pretty much what that website is promising.
As someone who at the time had a Pentium processor at 100Mhz and 32Mb of RAM, I feel confident enough to say that Winamp was lean as hell.
Random anecdote: I had a SNES emulator at the time that was fast enough to play "Zelda: Link to the Past" but only as long as I did it without sound. Winamp was fast enough that I could keep it playing in the background without slowing down the game.
If you had a 486-100 with 4 MB and playing MP3s and not noticing, that would be lean.
There were other players out there. I remember using K-Jofol, but I don't remember if it had a reputation for being leaner or just having wild skins. I know mpg321 exists which is integer only decoding for speed (it made a difference on my super low end box), but I don't know if it was available at the right time.
The OS got in my way, rather than the player, trying to use 486 machines as mp3 "jukeboxes" back in the day—"the day" being when high-hundreds Mhz single-core machines were the norm, and 486s could be had at garage sales and such practically for free.
MP3 playback would pop and skip if anything else tried to touch the CPU, under Linux or Windows, even on Pentium machines (there weren't 30 background processes of dubious value constantly begging for time like on a "modern" OS, so this rarely happened unless you tried to do other stuff while the music was playing). Choice of player didn't make much difference. Contrary to common wisdom, Linux was, if anything, even worse about this than Windows, but neither was good. QNX or BeOS, however, could handle MP3 playback while multitasking and web browsing without any glitches, even on a 486—though I don't know if I ever tried with RAM as low as 4MB, most likely 16MB was about as low as I went, since I had several of these systems and was able to assemble a couple really good ones by borrowing parts from others.
What MP3 players? Windows Media Player with the MP3 codec installed on your system? I don't recall there being a lot of options for Windows, at the time.
There were a few options. Napster for one. It's just the reason we don't remember is because we all installed Winamp and forgot about the rest. I spent more time looking for skins for Winamp that I did a replacement for it.
https://skins.webamp.org/ shows what the UI/UX was for it. Which is basically an old version of the current website. Flashy and modern.