> TERMS OF USE: You are not authorized to access or query our Whois database through the use of electronic processes that are high-volume and automated except as reasonably necessary to register domain names or modify existing registrations...
Since they aren't registering domain names or modifying existing registrations, their use would be prohibited by these terms of use.
The project is for the express purpose of registering domain names. And the project only does queries as needed to verify domain ownership - falling under "reasonably necessary".
IANAL so my opinion means very little, but it seems like the TOS are targeted towards people who want to abuse the system for doing things like mass data collection, spamming, and other "bad behaviors". Not someone who wants to make sure domains are available for registration.
After all, how do the big players do it? Simply downloading the list of all valid domains even once a day would not be sufficient.
You don't need to actually care about what it says, just if there is a record returned or not.