DevTools: refactor overlay input handling

Routes each message type into its own method.

Change-Id: I8dacbc37d614794f6757d6b9c669fa751de5ab4d
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1525263
Reviewed-by: Alexei Filippov <alph@chromium.org>
Reviewed-by: Andrey Lushnikov <lushnikov@chromium.org>
Commit-Queue: Pavel Feldman <pfeldman@chromium.org>
Cr-Commit-Position: refs/heads/master@{#641086}
2 files changed