Why did it use its? If it is the best or finest one by itself, it doesn't have to use a comparative-nuance its. What do you mean by "at its finest"?
ex) ....With singing, dancing, and special effects, Cats is musical theater at its finest.
"at its best, at its worst, etc., to indicate that something or someone is as good, bad, etc., as possible ▪ This is baseball at its best. ▪ He's often rude, and last night he was at his worst." (Meriam-Webster)
In the same way we can say:
"This match will be football at its best."===> What is the best thing you expect from football? This match will satisfy you.
"This movie is cinema at its best." ===> What is the best thing you expect from cinema? This movie will satisfy you.