I believe it may be because χορτοφάγος is in agreement with the masculine gender (in this case, the pronoun αυτός). If we are talking about food (φαγητό) as in "This isn't vegetarian" where "food" is implied, then χορτοφάγος would decline to match the gender of φαγητό, which is neuter, giving χορτοφάγο.
The declension of χορτοφάγος - https://en.wiktionary.org/wiki/%CF%87%CE%BF%CF%81%CF%84%CE%BF%CF%86%CE%AC%CE%B3%CE%BF%CF%82
At least this is my best guess. I'm not fluent in Greek, but I know that Greek has declensions.
It appears that αυτός (where it means "this") also declines according to gender, number, and case - https://en.wiktionary.org/wiki/%CE%B1%CF%85%CF%84%CF%8C%CF%82
As I have understood, if Greek wants to say "This is not a vegetarian", he would say "Αυτός δεν είναι χορτοφάγος". But if he wants to say "He/she is not a vegetarian", he would just say "Δεν είναι χορτοφάγος", because pronouns in Greek speech are usual omitted.
I'm not a native speaker, so I will be very thankful to any native Greek for commenting this suggestion :)