Yes, do interface both pieces. You’ll want the extra structure.
What you’re seeing in that illustration is the stitching on either side of the set-in placket. Typically a set-in placket is topstitched on either side. If you’re choosing the continuous (cut-on) placket, it is traditionally topstitched only on the innermost fold. You can do it however you want, but that’s how it’s usually done.
And yes, you can absolutely use the burrito method. I prefer not to use it for shirts because the yoke tends to bubble a bit if it’s not sewn perfectly–the yoke facing needs to be slightly shorter to account for the curve of the shoulder, and it’s difficult if not impossible to account for this perfectly when you’re sewing the burrito method. But please feel free to sew it how you prefer–that’s the beauty of sewing–there isn’t necessarily a right or wrong way.
Cheers.