Their direct wording is any business involved in the transmission of Bitcoin to a New York resident requires a license. Transmission has no exemptions for mining. Now, if you're *solo mining* in New York, you wouldn't need one, since you're not transmitting to anybody. If BTC Guild used coinbase payouts, it would also be able to bypass this, with one exception: There is no pool doing coinbase payouts (other than p2pool which is not exactly a pool) that doesn't require a failsafe wallet to catch dust/errors, and running a manual fix to distribute the dust/errors later is transmission. Unless BTC Guild turned itself into p2pool by setting a minimum share difficulty high enough that you would always have enough work in the PPLNS system to receive a payout, it's not an option.
Obviously you can't do anything about VPNs, but all accounts will be required to agree to an updated TOS affirming they are not residents of New York, on top of the Geo-IP ban to anybody accessing the site from New York.
And even then you likely have all sort of edge cases such as New York residents with miners co-located out of state or even non New York residents with miners co-located in New York. Rather than outright Geo-IP ban you could separate New York to a coinbase payout system separate from the main pool, since there would be less users per block solve dealing with dust may not be a problem.