As an FYI, I don't see this exactly. The fedback is a little confusing:
- alt+shift+l
- <enter>

result:
"window, new tab, tab"

expected:
Search your device... text field...

I have a fix for this.

Note there has been some churn in ARC++ focus handling, so that may have been part of the issue.

Chrome: 69.0.3480.0 Canary
With new tab page open, open the playstore and immediately press ctrl+search+left arrow focus jumps to the open new tab page instead of the top of the playstore.

Alt+tab back to the playstore, navigation with search+left/right doesn't work as usual.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/aeb1a5360b432c8fd16c072d89c27cc46262e0f7

commit aeb1a5360b432c8fd16c072d89c27cc46262e0f7
Author: David Tseng <dtseng@chromium.org>
Date: Tue Jul 10 19:09:50 2018

Remove chrome.windows.onFocusChanged listener

Test: manual.
Bug: 857540
Cq-Include-Trybots: luci.chromium.try:closure_compilation
Change-Id: I50532c92c750ceb37ace2c8ec01b2eb3d572525c
Reviewed-on: https://chromium-review.googlesource.com/1130014
Reviewed-by: Dominic Mazzoni <dmazzoni@chromium.org>
Commit-Queue: David Tseng <dtseng@chromium.org>
Cr-Commit-Position: refs/heads/master@{#573847}
[modify] https://crrev.com/aeb1a5360b432c8fd16c072d89c27cc46262e0f7/chrome/browser/resources/chromeos/chromevox/chromevox/background/tabs_api_handler.js

The confusing feedback in speech is now fixed. Marking as fixed for now and for you to verify. Thanks.

Chrome: 70.0.3530.0

Steps to repro:
# Close all tabs
# Open a new tab
# With Chromevox enabled, launch the playstore
# Navigate with search+left and search+right until Chromevox says 'Playstore, window'
# Press ctrl+search+left arrow
# Navigate with search+right arrow
# Notice that you do not return to the play store app, but are in the NTP

Expected: Chromevox is restricted to the current app

Actual: Focus seems to jump out of the app, but tab doesn't actually move where Chromevox is reading

I'm still not reproducing this. Could you try and come up with a more detailed reproduction or a different one? I did exactly the keys you stated (including ctrl+search+left).