OP says
"The dimensions.. are..: 20.6" long x 15.8" wide x 5.1" tall"

AA says
22" long x 14" wide x 9" tall

Does this disqualify the box since it is 1.8 inches too wide?

Also note

At some airports, carry-on baggage may be more restricted.
Additional limits may be placed on carry-on bags because of aircraft stowage capacity.
Limits may be imposed after the boarding process has begun.