More efficient answer 

What you wrote in this edit blindsided me so completely that it was hard to understand where you were coming from and so to write an efficiently worded reply.  It's not easy for me to grasp that there could be such a point of view as the one you seem to express.  But having pondered it for some time since you wrote this, I think I can attempt a clear, short, and direct reply.  You wrote:
 
 Sorry if this seems stupid, but I don't know why this article exists. Do we also need to prove that 4 is bigger than 3? That 50 is bigger than 1.2? No.
 
The facts are:
 22/7, rounded to the nearest ten-thousandth, is 3.1429.
 It is trivial to demonstrate that fact.
 π, rounded to the nearest ten-thousandth, is 3.1416.
 That 3.1429 > 3.1416 is a triviality, not worth an article.
 BUT: The fact that π is approximately 3.1416 can be seen only be first doing quite a lot of work, some of it relying on methods that are relatively sophisticated by comparison to the bare statement that π is the ratio of the circumference of a circle to the diameter, or the like.
 By contrast, the proof given in the article shows that 22/7 > π in a way that is quick and simple, unlike all the work needed to see that π is approximately 3.1416, so you can see that 22/7 > π while skipping all the labor involved in seeing that π is about 3.1416.
 ...and the method by which it is done, in addition to being so short and simple, is elegant, immediately startling, and potentially enlightening in that you immediately wonder if it fits into some larger pattern that would give you insights not otherwise available.
 
You almost seem to treat the fact that π is approximately 3.1416 as if it were self-evident, rather than something that can be seen only at considerable expense.