not for "beef" as a "complaint" - only for "beef" as "yell"

That was Beef - 5, Beef - 6 is given as "To Complain." Recorded back to 1880.

OED Supplement gives an 1888 citation: He'll beef and kick like a steer an' let on he won't never wear 'em for its definition, to complain, grumble, protest.