I'm curious, is the resemblance to kutembea just coincidental, or is there an etymological reason for it?
It's the applicative form (called the prepositional form in this course) of kutembea. It's basically like "to walk for/to".
The resemblance is not coincidental. The suffix -le has a prepositional value. Depending on the preceding letter the suffix can be -e , -i or -li. For exemple "kuchezea" means "to play with" , from "kucheza" "to play"; "kusomea" means "to study for", from " kusoma" "to read, to study". They also call it the applicative suffix