Google Released New Feature to Install Apps Directly From Search Results, in Google APP : Know How to Get It
What's New & How to get this new feature :
You can test this yourself by opening the Google app and searching for the name of an app. It will appear at the top of the results with an install button—this part is true for everyone. However, most people are booted into the Play Store when they tap it. Those with the new feature will see a permission popup just like they would in the Play Store, then a miniature Play Store frame appears so it can be installed. It's really neat.
This might only work from the Google app, not Chrome (that's common with similar features). Some users report that this started happening a month ago or more, but only recently has it started appearing widely enough that we got tipped about it. Take a look at your search results and you might find it's already live for you.
Or update your Google search App with below version to get this feature.
Download Latest Google App APK From here
Google App 188.8.131.52.arm
Google App 184.108.40.206.arm64