They made it into a ringtone because it was old enough to be public domain, and Nokia (I think?) didn’t want to have to pay royalties.
… I like the full version.
So fun fact: This is the “Ringtone Waltz” by resident Canadian Piano Virtuoso Marc-André Hamelin.
In turn the Ringtone Waltz is a remix of the Nokia Ringtone.
The Nokia Ringtone is a sample from the Gran Vals for classical guitar by Francisco Tárrega.
You’re listing to a remix of a ringtone sampled from a classical guitar piece and I think that’s cool as fuck.
Here’s the Gran Vals by Francisco Tárrega himself, composed in 1902. Give it a listen; it’s gorgeously soothing:
ETA: Also, the full name of the piano piece in OP is “Valse Irritation d’après Nokia (The Ringtone Waltz)”. Yup, he was so annoyed by cellphones ringing during concerts, he wrote a whole piano piece about it XD. You can hear him talk about it here: