Unable to reproduce this issue on Ubuntu 14.04, Win-10 and Mac 10.12.2 using chrome reported version #55.0.2883.75, latest stable #55.0.2883.87 and latest canary #58.0.2990.0.
Attached a screen cast for your reference.

Following are the steps followed to reproduce the issue.
------------
1. Opened chrome browser.
2. Navigated to URL: https://chrome.google.com/webstore/detail/line/menkifleemblimdogmoihpfopnplikde?utm_source=chrome-ntp-icon
3. It got downloaded and got added to the list of apps.

Reporter@ - Could you please check this issue on latest stable #55.0.2883.87 by creating a new profile without any apps and extensions and please let us know if the issue still persist or not.

Thanks...!!

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It turns out it is all related to
$ zcat /usr/share/doc/chromium/NEWS.Debian.gz 
chromium-browser (55.0.2883.75-4) unstable; urgency=medium

  * External extensions are now disabled by default.  Chromium will only load
    extensions that are explicitly specified with the --load-extension command
    line option passed into CHROMIUM_FLAGS.  See the chromium-lwn4chrome
    package for an example of how to do this.
  * You can also use the --enable-remote-extensions command line argument to
    chromium, which will bypass this restriction.

 -- Michael Gilbert <mgilbert@debian.org>  Mon, 02 Jan 2017 02:42:29 +0000

Even just browsing chrome://apps/ ,
with
$ chromium --enable-remote-extensions
all my apps are there.
Without it, there is only one app, "Web Store".

Well I can accept the phase out,
but at least the user should be shown some message on the screen
about why things are broken.

In fact you might as well get rid of the "Apps" bookmark at the top left when users start the browser... (but make sure chrome://apps still works for a while!)

Thank you for providing more feedback. Adding requester "krajshree@chromium.org" for another review and adding "Needs-Review" label for tracking.

For more details visit https://www.chromium.org/issue-tracking/autotriage - Your friendly Sheriffbot

 Issue 688606  has been merged into this issue.

 Issue 688865  has been merged into this issue.

Look like the installation of extension is broken in Debian Linux Kali since M55 (as per issue:688606). Unfortunately the team do not have a Kali Linux environment for a repro.

jidanni@ would you mind trying a bisect to find the exact regression range. Instruction here: https://www.chromium.org/developers/bisect-builds-py.

I am not sure whom to assign.Tom did some recent changes in/linux/debian/ so reaching out to him to find a owner for this issue.

M56 is already in stable, so it would be good to have a fix before M57 hits stable.

According to #3, extensions are disabled in chromium_browser by Debian.  This issue should not reproduce with google-chrome-stable, as it won't have the Debian patch applied.

OP, please let me know if you're able to repro on google-chrome-stable so I can reopen.

I just think some message should appear on the screen else the user thinks it is a bug.

#10, it does not repro on google-chrome-stable.
I uninstalled chromium completely and purged.
Installed google-chrome-stable Version 56.0.2924.87 (64-bit) and was able to install extensions again.
Any idea why Debian would block installing extensions?