The blockchain look up would happen on the Zilliqa platform but Unstoppable is building the software to make this process seamless to integrate for wallets and exchanges.
By integrating Unstoppable tech these wallets and exchanges can easily allow .zil integrations on their platforms.
We like to think of it similarly to what Stripe did for traditional payments. Their technology allowed anyone to turn an iPad into a PoS system. Unstoppable tech will allow any crypto wallet or exchange to integrate .zil to replace the address with human-readable names.