Migrate FILE WebThread getter to new Task Runner API

Bug: 667892
Change-Id: Ie91699d5b921213e3606b2a81225d5a96ecc415a
Reviewed-on: https://chromium-review.googlesource.com/596496
Commit-Queue: Mike Dougherty <michaeldo@chromium.org>
Reviewed-by: Rohit Rao (ping after 24h) <rohitrao@chromium.org>
Cr-Commit-Position: refs/heads/master@{#492787}
3 files changed