You are right, getting Google search results to deep-link into your app is achievable using only Universal Links and having your web content naturally feature in Google search results.
The Google documentation isn't great, but there are two major reasons you'd want to integrate the Google App Indexing SDK:
The first, as the documentation does say, is so that Google ranks your 'app content' higher in Google search results than if you didn't integrate the SDK. My guess is that 'app content' here is defined as your web content with app related meta data, such as the <link rel=alternate>
tag specified in the documentation. I've yet to find any way to validate/verify to what degree this helps - we have to trust the documentation for now.
The second is that currently, your deep-linking will only work from Safari Mobile. To facilitate deep-linking from Google search results into your app in Chrome for iOS will require implementation of Google's SDK, which will also provision a "back to Google" button in your app. To see whether this is worth doing you'd have to check your analytics to see how many of your iOS users are using Chrome instead of Safari Mobile as their main browser on iPhone.
Source for second reason: https://www.youtube.com/watch?v=6NFRNamQGCc&feature=youtu.be&t=268