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BrowserPlugin is only on on Chrome desktop and and surface sync is always
on on desktop. This CL deletes the old code path.

Bug: 672962
Change-Id: If0394bd7b8eed4b04d23fede8e31aff1ee3417b4
Reviewed-on: https://chromium-review.googlesource.com/1234323Reviewed-by: Ken Buchanan <kenrb@chromium.org>
Reviewed-by: Saman Sami <samans@chromium.org>
Reviewed-by: James MacLean <wjmaclean@chromium.org>
Commit-Queue: Fady Samuel <fsamuel@chromium.org>
Cr-Commit-Position: refs/heads/master@{#592497}