I guess it means more or less the same, but it is better to stick to a more literal translation.
It is important to note than eten is not a verb here. Instead it is a noun, meaning "food". Your suggestion would be translated as: "Zij hebben niet veel te eten." Here eten is the infinitive form of the verb "to eat".
Have you never heard the expression "I love you that much!" with arms outstretched as far as possible. It means "so much that I can't even show you, but I'll try." I consider it to be even more than "so much", but really it is the same idea. The negative to me would appear as less but really you could use both in the same situation. There is a different flavor to it though. Someone told me that they do have plenty of food.. No, they do not have so much food. "So much" is a comparison to what may have been said before or it could be qualified with a clause afterwards. "That much" is also a comparison, but to a physical amount that could be shown.
"That" can be used as a conjunction, a demonstrative pronoun and an adjective. Scroll past the definitions until you get to the adjective and look at meaning 1c in the Merriam-Webster dictionary. You will find that the adjective "that" can mean "So great a" .or "such".
Countvlad could try reporting it. It may be though that Dutch may have a different expression to match "that much" as well.
Ah! "So much" is the definition which depends on what the comparison is to. "So much" is really closer to the second and "that much" to the first without further information. Less than what? Less than they thought, but we don't know if they thought they had a lot or a little and it is less than that. This is ambiguous in Dutch as well.