Yes, I know about that POSTMAN used to run inside a tab, but it seems to have been abandoned for quite some time. I still have it installed, but it still telling to to 'upgrade' to the packaged app.
That Postman extension that you linked, I actually didn't know about this before, but that doesn't seems like something provided by the original developer. Any idea whats the story behind it? EDIT: Nevermind, just Googled the domain. Its the same developer.
The earlier app ran as a "legacy" Chrome app. Chrome has deprecated those style of apps and it's not accepting new submissions for legacy apps. I can only push updates now.
The newer style Chrome apps run in a sandbox and have access to better APIs. This allows Postman to have features like collection runner, test scripts, OAuth 2 etc. Unfortunately, window management is a bit screwed up and am hoping support improves there from Chrome's side.
Edit: here it is, both the extension (tab) and the packaged app (window): https://chrome.google.com/webstore/search/postman?hl=en