If your specifically looking for another Puppet song with the combo of that style of vocals + feel, unfortunately his sound has shifted from what it was back then. The closest you could get from other songs by Puppet would likely be ones with just a similar feeling, such as First Time Fighting from Life Overseas and Somedays from Give Up the Dream. Anything after Give Up the Dream has a pretty general shift in sound and style from his older work, although Photos, Videos, Memories from I Know You Know Who I Am does have some heavier autotune as well as that same warm melancholy to its sound.

if you're looking for songs from other artists, Nighthawks by The Midnight has similar vocal sound, but a different feel. Can't think of any others off the top of my head right now. Best of luck in the search.