"The vegetarians eat in the restaurant."
Translation:La vegetaranoj manĝas en la restoracio.
If you, in normal conversation, choose to use the expression «legom-manĝanto» or «Legommanĝismo» you may well be very understood. But why the word «vegetarano»? for that I consulted the Plena Ilustrita Vortaro (a very good book which I recommend ALL acquire at least one copy of) and find that vegetarano is associated with the root "vegeti" (my translation of the definition follows, you've been warned) to fulfill the functions of nutrition, growth and maturation, which consists of the life of (~aĵo) a thing. (other definitions how different affixes alter the meaning. then finally, after the suffixes we want) Pridieta doktrino, kiu malkonsilas nutri sin per ĉia animaldevina nutraĵo. a dietary doctrine which counsels against the consumption of all kinds of animal derived foodstuffs
So the words comes from different roots, and, in fact, Esperanto recognizes «vegetaĵo» as a legitimate word. It seems to be, in fact, the scientific word for the class of living things we mundanely call "plants." Similarly «Animalo» is that class of living things which are generally self-mobile. «Besto» is the everyday word, probably derived from some Germanic source. «Vegetarano» is thus, not so far fetched as one may think.
But it does cause me to marvel at how much thinking Zamenhof put into this.
Just to add to that as a German, besto most likely derives from the same root as the English "beast" or similarly the German "biest" (pronounced the same). I think it was chosen because it's shorter than animalo (although that is now being used, too). The German everyday word for animal is "Tier", by the way.
The vegetarians are the subject and their meals is the direct object (but is not directly mentioned). Think of it as "La vegetaranoj manĝas manĝojn en la restoracio." Otherwise, they would be eating the restaurant.
(But that would be okay, because very few restaurants are made of meat...)