Why is this example a regular language?
Pumping lemma is not a sufficient condition for being regular, it is only a necessarily condition. Satisfying it does not imply that the language is regular.
In the pumping lemma, some parameters are chosen adversarily, i.e. you don't have control over them. If a language is regular then pumping lemma says that "for a long enough string in the language there is a partition s.t. ...". To show that a language is not regular you should show that for all ways of partitioning the conditions will not hold. Your argument does rule out $y=11$ for example, you are only talking about a particular way of partitioning and that does not imply anything.
The language is indeed regular, it is (11)*.