If you downloaded the Camera app from outside the Play Store it's likely that it's a modified version of the app. The modifications prevent it from installing as an update to the existing camera app so it must be installed alongside it.
I hope you got it from a reputable source.
PS: The first-gen Pixel will not get an official update to enable Portrait Mode with the rear camera as that requires special DPAF hardware that is only included in the Pixel 2 and later models.