Is the intent of this sentence to mean the boy will never again eat any future dinners, or is it intended to mean the boy has finished eating this dinner but has perhaps left food on the plate? To me there is a difference in saying not eating dinner anymore (giving up this meal for ever more) and not eating anymore dinner (being full).
The boy has finished eating his dinner and therefore is doing something else now.
I guess it technically possible to interpret it as "he said he will not be eating dinner at all starting now", but it wouldn't even cross my mind without some further context.
To be sure that 'he won't be eating dinner at all starting now', you can use the habitual verb "jadać" (nie jada już kolacji).