- Interpretation of character is a form of literary analysis
It's as simple as that.
I highly recommend taking a look at Stella Adler on Ibsen, Strindberg, and Chekhov which demonstrates how literary analysis is critical in creating believable performances.
Poetry long pre-dates the modern novel, and dramatic poetry was held in the highest regard in antiquity, even above the epics. Modernism in theater was a centrally important literary movement, that influences all other forms of art and literature. Likewise, Shakespeare's impact on literature, drama and the English language is profound.
Theater is unique in that analysis extends into performance, thus dramaturgy in addition to acting and directing.
In relation the the question that prompted this meta, I'll compare portrayal of Richard III and Laura from the Glass Menagerie. Both have a physical impairment that influence their characters.
-If the deformity is pronounced physically in performance, as is generally the case, the audience interpretation is that the physical condition drives the character.
-If the deformity is downplayed, as with the Olivier, the audience interpretation is that the character is burdened more by the psychological effects than the physical. (i.e. the deformity looms much larger in their mind that the physical actuality.)
The latter case may be considered much more complex.