The informative "addition" is on the word-gi is suffixed to. Thereforesullegi ("to you, too") in the example means that "you" is not the only one to whom "Happy New Year" is wished.
This form is used after voiced consonants and vowels. After voiceless consonants (note:g,b,d,z, andž are voiceless), the form-ki is used.
-gi is more specific than-di.-gi refers to a specific place within a generalized location marked by-di. The approximate location with-di comes first, followed by the specific-gi.