So long as there's no damage to the laptop and you can honestly say you've used it as it was intended to be used, it should be covered. I see no valid argument from their side - the issue has been caused by one or more of; poor quality components, poor workmanship, poor QA, or a design flaw.
As far as I see it, this issue breaks the 'fit for purpose' quality standard, based on Apple's own definition of 'fit for purpose' - the 2013 MBP is not considered "obsolete" by Apple themselves, yet yours is being rendered unusable prematurely.
It goes without saying that when you visit the store, be polite and don't start throwing rights around! There's a chance they'll resolve it for you without the awkward rights discussion.