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Then how could St Genesius be a saint?  

First of all, Genesius would be an example of Baptism of Blood, whereas this thread deals with Baptism of Desire.

St. Genesius was baptized.  It was during his performance ridiculing the sacrament of baptism that he had his conversion.  During the play, after a flood of grace, he asked his fellow actor to baptize him.  This occurred publicly, in front of the emperor.  It was this incident that brought about his martyrdom.

Some people would argue that there was not sufficient intent on the part of the actor performing the Baptism to qualify as valid intention.  I think that's debatable.  If he thought he was DOING a ceremony DONE by the Church, I argue that it was valid.  Church has never stated that the person baptizing must believe in the effect of the Sacrament, which is why even atheists can validly baptize.

They must intend to do what the Church does. If there is no intention as in a play then it is not baptism.

So St. Genesius had an outpouring of grace, converted from his paganism, and asked to be baptized, trusting in God to provide what was needed.  Is it your position that God gave St. Genesius the grace of conversion but neglected to give the grace necessary to the other actor to baptize with the basic intention of doing what the Church does?   Bear in mind that this is the same God who said "Unless a man be born again of water and the Holy Ghost, he shall not enter the Kingdom of God", and again "He that believeth and is baptized, shall be saved: but he that believeth not shall be condemned", and elsewhere: "Ask, and it shall be given you: seek, and you shall find: knock, and it shall be opened to you. For every one that asketh, receiveth: and he that seeketh, findeth: and to him that knocketh, it shall be opened. Or what man is there among you, of whom if his son shall ask bread, will he reach him a stone? Or if he shall ask him a fish, will he reach him a serpent?  If you then being evil, know how to give good gifts to your children: how much more will your Father who is in heaven, give good things to them that ask him?"

One of the biggest problems with those who deny EENS is a lack of faith in Divine Providence.  Not a single hair falls from your head without God willing it.  Not a single drop of water falls from the baptizing vessel without God directing it.