I think this is a list of the most popular songs of artists who have performed on the Kouhaku show itself. Although did Hikki ever perform on the Kouhaku? I'm not sure about this. I don't think the Orange Range and Ketsumeishi songs belong there, if it's an all-time list. More enka artists should be on the list.
This is not arranged according to rank or popularity or votes received. I think it's more like the songs are arranged using the alphabetical system of the Japanese language:
Anata ni... by Seiko Matsuda
Anata ni... by someone
Anata no Kiss o Kazoemashou by Yuki Koyanagi
Ano... by Akiko Wada
Abare... by Fumi someone
are all grouped togeter. Same goes for Ayu's songs. Dearest is with:
Departures by globe
Desire by Akina Nakamori
Tsugunai by Teresa Teng
and all the other "T" songs ("T" often becomes "D" in the Japanese language, for people who didn't know
)
Seasons is grouped with:
Sakuranbo by Ai Ohstuka
Secret Base by Zone
and all the other "S" songs
So nothing to worry about, Ayu fans!