He's talking about the normal flow of the site (click the big blue button at the bottom of the first page, then the second page). This leads to a "Login with Github/Google/Facebook" prompt that can't be skipped. You can close it, but that doesn't get you anywhere.
Please explain. Without maintaining that ordering, you're going to have to iterate over the entire stack after every pop, no? One of their requirements was to keep pop() at O(1) rather than O(n).