(reland) Check missing headers in the build on CQ

This script is run on the following bots on CQ:
- linux_chromium_dbg_ng
- linux_chromium_rel_ng

Note that this script can only be added to bots that have "all"
in "additional_compile_targets".

BUG=661774, 725877

Review-Url: https://codereview.chromium.org/2903733004
Cr-Commit-Position: refs/heads/master@{#474570}
4 files changed