Thanks for filing the issue...

Unable to reproduce the issue on reported chrome version 71.0.3578.98 using Windows 7 and 10. Attaching screen-cast for reference.
Steps: 
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1. Launched reported chrome 
2. clicked on gmail link and clicked on gmail app in APPs also clicked on search result 
As we have observed that the gmail got opened 

@Reporter: Request you to retry this issue with fresh profile without any extensions & apps or reset all the flags and let us know if issue still persists.

Thanks..!

I’ve done all that and my browser on my work computer still will not access
Gmail.  I continue to get the same error even after clearing browser
history, cookies, etc. and signing out and resetting the browser to initial
defaults.

Thank you for providing more feedback. Adding the requester to the cc list.

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

ERR_TUNNEL_CONNECTION_FAILED suggests you're using a Proxy - do you know if that's the case (e.g. you're an enterprise user)? If not, it may be a sign of malware improperly attempting to configure a proxy.

If you can attach more details as described at https://dev.chromium.org/for-testers/providing-network-details , this can help understand more about the proxy. Comment #2 tried to cover the most common cases for where proxy settings might come from, but with a full log, we can better try to pinpoint and help resolve the issue.

If this is happening in all browsers per the title, then this is a connectivity issue to resolve with your network admin and not a Chrome bug we can fix.

Please provide the requested NetLog or we will have to close this bug :(

Closing for lack of requested feedback.

Issue also appears to be non-specific to Chrome and thus almost certainly a connectivity issue with the user's local machine/network/proxy.