The straight rigid projection you're seeing in the frame you posted is the entoglossal process, which is a portion of the hyoid or hyobranchial apparatus. There are a few other components that make up the hyoid/hyobranchial apparatus in addition to the entoglossal process (ceratohyals, ceratobranchials, basihyal). The membrane you are seeing stretched over it is the tissue surrounding/covering the tongue retractor muscle, the hyoglossus. The hyoglossus muscle extends from the hyoid apparatus (on the ceratobranchials) to the accelerator muscle (the enlarged portion of the tongue before the tongue pad that is making contact with the prey. At rest, the accelerator muscle sits on/around the entoglossal process with the hyoglosses pleated up behind it like an accordion.
Chris