It does not, unless you are writing "What to eat" as a sentence you repeat to yourself over and over. The more proper way is "What do you want to eat" because you have a complete sentence: a verb (do) and a subject (you), with a prepositional phrase to clarify (to eat).

Occasionally, you will see "what to eat" used as a casual/informal way to say "what should we eat?" or "what should I eat"? A similar example: "What to do?" can be used if you are thinking about what plan of action to pursue, and you are suggesting to the listener that he/she offer ideas about what to do.

No! I see this error quite a bit. I don’t know what to eat. What do I eat? “What to eat” is NOT a question on its own.

I think you might mean "What's to eat?" which is a common way of asking somebody what they have for you to eat, i.e. the opposite of what you meant. "What to eat?" is possible but very odd - maybe a mad prince might ask this, and it isn't clear quite what it means, or whether it is the speaker or the listener who is hungry.