From the article:

"Even if one of the parties is dishonest and deviates from the protocol, that person cannot learn anything more than if x = y."

No. The two parties trust each other. This is to secure the fact that Alice and Bob are talking to each other and only know that x=y

no need if the protocol is "fair". He just gave a simplified example on how to solve the millionaire problem. There are many ways to solve it, some are unfair, some are fair.

For example you can use fully homomorphic encryption to trivially solve this problem.