Move WebUI's RegisterMessageCallback to use the new callbacks.

BUG=714018

Cq-Include-Trybots: master.tryserver.chromium.mac:ios-simulator-cronet;master.tryserver.chromium.mac:ios-simulator-full-configs
Change-Id: I2ca24193658c5d25d4038151b04b7216bb4bf2ba
Reviewed-on: https://chromium-review.googlesource.com/976392
Commit-Queue: Avi Drissman <avi@chromium.org>
Reviewed-by: Kyle Horimoto <khorimoto@chromium.org>
Reviewed-by: Scott Violet <sky@chromium.org>
Cr-Commit-Position: refs/heads/master@{#545658}
156 files changed