Migrate FILE WebThread getter to new Task Runner API

Bug: 667892
Change-Id: I3bc66e50af4df14bb9a371d2e586e1c8c9a8daf1
Reviewed-on: https://chromium-review.googlesource.com/609304
Reviewed-by: Rohit Rao (ping after 24h) <rohitrao@chromium.org>
Commit-Queue: Mike Dougherty <michaeldo@chromium.org>
Cr-Commit-Position: refs/heads/master@{#493754}
3 files changed