Most distributions do but I haven't tried.
Looks like you are having some download issues; some can be found as torrents which can be faster...
WOW that's bad. Found a year-old forum with a similar complaint. Nobody's gonna want to put up with that no matter how good the distribution is.
As one forum I checked said, you could probably accomplish the same with other distributions. There are 'small footprint' variations of Ubuntu for sure. They at least have a viable downloading process and 'live stick' options. The 'Computer Audiophile' forum site may have more support. Playing audio just isn't that difficult as modern computing goes (a Pi can do it ferfuxake); I think mainly you need to get out from under the Windows OS bloat with the old computer, and the right Linux is probably a good way to do that.Update:
Checked their website and apparently you can do a (presumably faster) paid download for 3.99 EUR ($4.61). I might still try one of the low-overhead Ubuntu variations though such as Lubuntu linux
Speaking of a Pi, if you already have the USB DAC, you can get a Pi setup running for <$100. Computer Audiophile would be a good resource on that too.