... it starts to get really noticable from 24 years and further on (snip)
(I believe Roy was joking about the music quality).
Either way... far as I can tell from that website, those songs have
not been distorted to simulate long propagation though interstellar space. So any difference you're hearing is just the quality of the original recording -- and maybe some static added.
But those space effects are real, and definitely affect signals that aliens might hear from Earth. Of course, it depends on their line-of-sight. Signals traveling through near-perfect vacuum wouldn't be distorted much. But signals traveling through long regions of ionized gas would get very distorted. It all depends on the space between us and them. So it's not the same for all alien "listeners".
Turns out, SETI researchers actually spend lots of effort trying to understand how alien broadcasts might sound to us, after propagating through different space environments. The effects (per length) are tiny, but the path lengths may be thousands of light years. So tiny effects add up.