Learn German: Das Alter spielt für diese Stelle keine Rolle. - Age does not matter for this position.

This is a common German idiom. The phrase eine Rolle spielen literally translates to playing a role, but it is the standard way to say that something matters or is important. To say something does not matter, you negate it to make keine Rolle spielen.

Why is it diese Stelle and what case is being used?

It is in the accusative case. The preposition für always forces the following noun into the accusative case. Because the word for position or job is feminine (die Stelle), the demonstrative pronoun for this becomes diese.

Could I use another word for job here, such as Beruf or Arbeit?

Stelle specifically means a position, post, or vacancy at a company, which makes the most sense in this context. Beruf refers to your overarching profession or trained career, while Arbeit is the general word for work. You could say für diesen Job informally, but für diese Stelle is the standard professional choice.

Why do we use keine to negate the sentence instead of nicht?