The person said “got to run out of stuff to burn someday” which kind of means that everything is destroyed, not just humanity. Without plant life, someone correct me if I’m wrong, but we’d no longer have an atmosphere.
Maybe we’d still have tardigrades or some shit, but I think “devoid of all life” would be pretty accurate in this scenario.
Generally speaking though, you’re correct that the planet will survive just fine (rather, it would probably thrive) without humans.