Exactly. It's one thing if the bad guy is going off to finish enacting their master plan or even if the bad guy is lazy and going off to do something more fun. This is the Kithrak's top priority. Furthermore, he says that he's leaving to tell his superior that the job is done. So he's leaving his subordinates to get the artefact and then...trek on foot to deliver it. Even if he didn't want to be involved or for his dragon to be involved, it would be faster and easier if he just stayed there, waited for the others to get the artefact, then flew with the artefact to deliver it.
I understand that sometimes characters need to do the illogical thing for the sake of the story, or certain things need to be fudged, etc. I'm even an advocate of not ketting hard logic detract from telling the best story possible. But when the flaw is this glaring and distracting, you can't just leave it in and say "it's just a story."