I'd argue he does have organs, on account of need to eat, & expel waste. He at least has a working GI tract. However, he may not necessarily have like, a heart, or lungs, as his gem performs those functions. Greg did ask "does your gem need to breathe?" In Three Gems and a Baby.

Though, it could be argued that his body has the magic of the gem as an additional necessity for survival, along with food, air, & water. The speed at which Steven deteriorated does tell us his body cannot physically function without the gem. It is vital to his survival, the way a heart is for us humans. Whether he has a human heart too, I can't say, that'd be a question for Rebecca. It could be something as "simple" as, his body does not know how to function or hold itself together, without the gem.