"Ja, ich gehe essen."
Here the infinitive form is used. The sentence is used to mean 'going out to eat'. Hence, 'gehe essen' which translates to going to eat.
'Yes, I go eat' is not standard English construction. The meaning might be understood, but it is a poorly constructed sentence. Check the conjugation forms given.
There is no 'going to'-future in German, no.
But there are verbs that are a construct of the infinitive of a verb + a form of 'gehen', like 'essen gehen' (= to eat out, to go for a meal), 'spazieren gehen' (= to take a walk, to go for a walk), 'schlafen gehen' (= to go to sleep). Those are all about moving somewhere or doing something.
So I guess, 'going to' is just the best way to translate that in the sentence.