Semantically, the connection is clear: when something stretches across a long distance, it becomes quite thin. PIE *t-n- also underlies English "thin" via Germanic and "tenuous" (stretched almost to the breaking point), "tense" (stretched out), "tent" (canvas stretched over poles) via Latin via French.
The difficulty isn't in the semantics, but in the phonology. Proto-Indo-European *n̥y generally turns into /anj/ and later /ajn/ in Ancient Greek, and (as fdb points out) there isn't a solid explanation of where the extra /i/ in the second syllable could have come from: the known rules would predict /tajna/ ταίνα. These are the unclear details Beekes is referring to.