I would like to know why there is no article (say "a") in front of the word "normal" in the phrase
A game in normal form?
This phrase is standard in game theory.
It's not that it's strictly incorrect to do so. It's just that it's more idiomatic to say "in normal form".
We don't say
the game is in the normal form
in game theory for the same reason that we don't say
the patient is in the surgery
in medicine. The articles are typically elided by native speakers.