Does 'meta name="google-play-app"' work?

Does this meta tag works in Android ? No.
Can it be handled ? Yes.

iOS 6 and later, natively shows a smart banner that reminds browser user, about the mobile application. But android doesn't support this natively.

To have this banner in android browsers you can use a jquery plugin: https://github.com/jasny/jquery.smartbanner

First add this:

<meta name="google-play-app" content="app-id=com.mygood.id">

Then include smart banner:

<link rel="stylesheet" href="jquery.smartbanner.css" type="text/css" media="screen">
<script src="//ajax.googleapis.com/ajax/libs/jquery/1.8/jquery.min.js"></script>
<script src="jquery.smartbanner.js"></script>

At last initialize it:

$.smartbanner({
  title: 'My good title',
  author: 'My smart author'
});

Source: http://www.dunnsolutions.com/content/application-development-blog/-/blogs/smart-app-banners-for-ios-and-android
Related: Creating an android smart app banner

You could look at adding this to your web app manifest instead. At least for Chrome and FireFox.

When adding the properties prefer_related_applications and related_applications along with name and icons you should get prompted.

Example copied from developer.google.com:

"prefer_related_applications": true,
"related_applications": [
  {
    "platform": "play",
    "id": "com.google.samples.apps.iosched"
  }
]