There is a committee of a small group of people who see all the shows and determine eligibility. Through a season, they announce what the final determinations are (ie that the four girls who play Matilda are not eligible, but will instead receive an Honor).
The based on those determinations, there is a separate small group of people who also see all of the shows and collectively decide who will be nominations. Those nominations are then announced (which happened earlier today).
Lastly, Broadway League members with "Tony Voter" status then (supposedly) see all the nominated shows (and have been doing so all season long) and must cast their ballot by a deadline. There is about 850 voters. Voters can also be from either of the two committees mentioned above.
The two committees have seen I'LL EAT YOU LAST, but the Voters will now have to buy tickets if they want to see it.
"The Spectacle has, indeed, an emotional attraction of its own, but, of all the parts, it is the least artistic, and connected least with the art of poetry. For the power of Tragedy, we may be sure, is felt even apart from representation and actors. Besides, the production of spectacular effects depends more on the art of the stage machinist than on that of the poet."
--Aristotle