Is the install button still consistently appearing for you right in Play Store search results?
"Google is constantly optimizing and tweaking its apps through various A/B tests, and the latest one for the Play Store has us scratching our heads quite a bit. We’ve noticed that the familiar and handy install button is disappearing for some in the Play Store’s search results, which means that you actually have to tap through to the full app listing to install an app. This behavior isn’t in place for all results and apps, though, making the tweak feel arbitrary and random..."
I have the update and it makes sense to me. I don't want to accidentally click install while scrolling through search results. The arrow functions as a drop down preview of the app for easy comparison. The install button is still there on the main app screen.
Installation is just the same as getting an app on desktop and telling it that yes, you do want to run it. (I know that sometimes requires a password, but sometimes it doesn't and I'm not sure why but that's how Android Play Store installations work).