Even though you are right and it is certainly not necessary to use an MVC framework to build a web-app such as this, you'll have to agree that the thoughts behind using such a framework are important (data/code/interface separation). But that doesn't mean MVC is a hammer for any nail.
Except that this webapp is absolutely built with an MVC framework — it's just that the M, V, and C are in different places than they are in the dogmatic arrangement.
MVC is not a fixed design, it's a legitimate universal Design Pattern (unlike most of the GoF book). It's a shared nomenclature for describing the arrangement of concerns, not a prescriptive blueprint.