Do you use any apps like CF.lumen, f.lux, or Twilight to adjust your screen color, or any other apps which add floating buttons to your screen? Such apps operate through the use of overlays, and Android won't allow you to tap the Install button while those overlays are active.
You can check if this might be the case by going to Settings > Apps > gear icon > Special access > Draw over other apps. If you have any apps with that permission granted, try disabling the permission to see if the Install button becomes actionable.