To surpass all competitors. The allusion is to a cake-walk. TAKE THE RAG (q.v.) is an earlier phrase.

1

1886.  As a purveyor of light literature,… Mr. Norris takes the cake.Pall Mall Gazette, Sept. 2. (N.E.D.)

2

[See Notes and Queries, 8 S. i. 69, 176, 364.]

3