Legal Question in Landlord & Tenant Law in Nevada

I sounds like you have thought this through and have your own argument well in hand. Upon signing a lease for a 60-day term, you notified the landlord you intended to vacate in 60 days. If they use the same form for all leases, including those of a year or more, the "standard clause" regarding 60 days' notice seems irrelevant to your particular situation. You did, in fact, notify them - in writing - of your intention to relinquish the property after 60 days. It was inherent in the contract, so any further notice would be redundant and superfluous.

Now, there may be some other language in your lease that contradicts this logical argument, such as an automatic renewal provision, extensions upon expiration of the initial term and thereafter, etc. If they set themselves up to enable a discretionary eviction at the end of 60 days, the 60 days' notice requirement may hold up more in their favor.

So, here is your practical solution: Threaten to take them to Small Claims Court to have a judge decide if their very unusual provision and requirement is legally enforceable. Tell them you are not afraid to drag them through the legal system to find justice and will make trips back to Reno for appearances as necessary. They can either step aside with their odd position or prepare to fight it out with you, as you do not intend to hold the apartment beyond 60 days or to pay any more than you originally obligated to pay under the contract. If they insist on going forward with collection efforts, you must be prepared to make good on your threat, though, so you may be facing some minor hardship keeping them from hurting your credit rating or otherwise causing you trouble. I think you have the winning argument (provided there are not some other governing clauses in the contract that make them right in their position), so don't hesitate to stand up for yourself!