There are severaly types of energy - kinetic, heat, etc...
Food if fuel for the body - it needs nutrients to keep it's growth, to generate new cells, etc.
Heat is the product of kinetic energy that is again the product of moving muscles and blood flow.
While our body functions are controled by electroical impulses, you can't just eat energy, and genetic modification in that direction are ilarious to say the least.
and kitoftheworld said, there was food in some shivan containers, thus tehy eat.
It's only, er, 'ilarious' if you wish to apply it to present day human physiology. With something like the Shivans - whether built from scratch by a designed or evolved over many years (i.e. of adding technology and genetic engineering) - it becomes more plausible. Particularly given their - suggested - organic fusion capacity.
I'd note that kinetic energy is produced through friction, so you get that (and heat) from any mechanical object anyways. Muscle movement in particular IIRC is caused as a result of the activation of certain proteins in the muscle via electrical impulses. Nutrients... the main issue IMO is the ingestion of nutrients used to get chemicals not naturally produced by the body. However, this does not preclude an engineered solution to produce these chemicals internally. Stuff like growth, movement, etc could all be powered using some form of 'direct' energy source.
Remember this is sci-fi, after all; there's no reason why it couldn't happen, and I guess the main reason is which is more likely. To me, the Shivans seem more likely to be 'powered' in this way then through conventional eatery - largely because of their apparent lack of interest in resources like planets (this would obviously depend on what they eat), and the suggestion of some form of electrical/energy source within them from the Hallfight ani. It's not necessary to assume the Shivans were always 'designed' this way, of course.
I can't remember the mission with 'Shivan food'. Albiet I'm not sure we should always be regarding the content of containers as deadly serious canon, given those in the last mission of FS1 (and how would the GTVA identify Shivan food?).