"to their purpose" is correct... "purpose" is not "behind" "their", is "after" "purposes" is plural... In this case the plural has no sense, because is a general phrase. Regards!

I think the sentence sounds bit strange to me but I think their can be replaced with "its" and that is singular as well as "albatross" and "is". To me the sky has only one purpose for birds unlike a broom that can be used for house or general floor cleaning, playing a game called broom ball that is played on the ice, and can be to prop doors open or closed, which would be purposes. gliders as it is comparing albatross to other flying and gliding birds and animals so that needs to be gliders.

"Harness the sky to their purpose" does not make sense.