In the words of Olivier himself:
"It's called acting."
This quip derives from a very famous anecdote about acting technique, which reportedly occurred on the set of Marathon Man. Dustin Hoffman, having stayed up for days to be able to convey his character's exhaustion and confusion, seeing Olivier sitting comfortably in his chair, waiting to shoot, asked Olivier how he was able to make his own performance so real. Olivier is said to have replied: "Dear boy, it's called acting — you should try it."
This anecdote is primarily a comment on the divide between method acting, in particular as taught by Strasberg, and the more traditional, but highly rigorous and effective RSC training.
However, it may shed light on Olivier's choice to downplay the outward deformity--Olivier was considered the greatest actor of his age and his Richard III film portrayal probably still ranks at the top.
- Olivier downplayed the humpback because he could--he's that good
Relying on a prosthesis to define the character could be regarded as a crutch, not required for an actor of such consummate skill.
To emphasize the points in this answer, 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.