I'm not really seeing the problem? Design is lineart, palette and markings, not just lineart. As long as they're not using the same palette and markings as the one you got, each design is still a one-off.

"- Once this adopt is yours you're free to do whatever to the design, make changes, swap the gender, your choice since this character is all yours now! Have fun."

This doesn't state that the lineart won't be reused. Unless that was specifically stated, I don't think the artist is in the wrong.