(Edited to reflect the uncertainty about the exact situation)
Note : not a QSA, just have some PCI experience
PCI DSS is a standard set by the payment companies - VISA, MasterCard and the rest. In general, it does not have the force of government regulations (though some state laws, I believe, reference it - consult your local lawyer). Rather, the Payment Companies require you to comply with the PCI (whether you need to be certified varies on your situation) when you have a relationship with them (directly or indirectly) to process cards. The way they can force you to comply is to, again directly or indirectly, prevent you from processing cards if you do not.
If you are not processing cards, if you are purely client, if you do not have this relationship with them (or a relationship with a card processing service provider that has a relationship with them), then they cannot require you to comply with it.
However, that said, the PCI DSS is a GOOD standard - you should be doing at least what it says if you're handling credit card numbers (PAN) as far as security. As well, PAN are considered Personal Identifying Information (PII) for almost all PII statutes I am aware of. That means that if you handle credit card numbers, you need to comply with all the PII rules. Again, your local statutes may apply here (as may the local statutes of your clients...)
If you are a merchant and providing the app, you need to comply with PCI if you are going to remember/store credit card numbers, even client side. If you are not a merchant, you probably still should, but may not legally have to. Fuzzy.