This is definitely being done for a reason. One of the best ways to increase user clicks on a particular link is to remove all the other links on a page.
This case is a bit extreme: Instagram has removed most links not only for mobile web browsers, but also for desktop users. That said, the reason for removing it from desktop browsers may also extend to privacy: I personally really like it that it's not easy to find links to my Instagram posts. Privacy through obfuscation, I suppose.
In any case, Instagram's web presence really encourages users to download the app. That's smart, as that's where Facebook is the weakest... so Instagram was able to focus its (very) limited resources in the one place where it could really shine.
This case is a bit extreme: Instagram has removed most links not only for mobile web browsers, but also for desktop users. That said, the reason for removing it from desktop browsers may also extend to privacy: I personally really like it that it's not easy to find links to my Instagram posts. Privacy through obfuscation, I suppose.
In any case, Instagram's web presence really encourages users to download the app. That's smart, as that's where Facebook is the weakest... so Instagram was able to focus its (very) limited resources in the one place where it could really shine.