What is the purpose of having this face in the subtitles/lyrics?
Possibly to show the reaction of the actor in the song, which seem to be surprised/heavily pressured by fact of &quot;the demon who wears goddess mask&quot;... maybe... or probably there's no purpose of the kaomoji!.. or it can be anything...
Considering that KOTOKO is a famous denpa song artist (read also What is the actual meaning of &quot;denpa&quot;?), anything goes. (Note: the Japanese title even has a star in it: 七転八起☆至上主義!)
So, what is a denpa song?

Denpa song (電波ソング) is a type of Japanese music that is intentionally strange and catchy. Common features of denpa songs include intentionally off-key vocals, nonsensical lyrics and an over-the-top tune.

Back to kaomoji...
Kaomoji is certainly rare in song lyrics, but there are some more (not necessarily denpa song). From Yahoo! Chiebukuro:


Koi no Tsubomi: (T_T), (&gt;_&lt;), (*_*), (;_;), (T^T), (T0T)/, (*_*)
Love Love Chu Chu!: (&gt;&lt;), (T_T), (#^_^#), (@_@)
Happy Succession: (^^;), (T_T)
girls: (&gt;_&lt;;), (≧O≦)
message: (-.-;)', !(&gt;&lt;)!'

(All links are link to song lyric)

Last but not least, Ryuichi Kawamura has a song titled 〔&gt;_&lt;〕.

Personally, I don't consider Shichitenhakki Shijou Shugi! as denpa song, but perhaps it's because I'm already used to IOSYS.