Question regarding Yankees-E. 153rd Station during Game Days

From the MTA website:

FARE PAYMENT
Ticket collectors will be posted on the station mezzanine level. Customers must show a rail ticket to exit the station and proceed to the game, or to access the station platforms and board trains after the game. Please hold on to your ticket throughout your travel time to and from the game.

Since you can buy and use a 1-way ticket, and use it to get there even if it is a game day, what happens then? Do they punch the ticket, give it to you? Do the ticket collectors take those numbered strips of paper you get back when a ticket is collected by the conductor? And if the former, what if you use a 1-way to a station beyond E. 153rd, and make no mention you are getting off at that station on a game day? I tried searching, but never found an answer to this, and I am curious - purely out of curiosity about random things I guess.

You get the ticket back from the conductor on the train and it has to be punched once more by the conductor at the station gate to officially kill the ride. Seat checks cannot be used as proof of payment, you need the ticket. The conductors are made aware on game days for which trains these rules apply. Thus these procedures are not done when gate collection is not in effect.

Just to add, if the ticket was only punched once, doesn't mean you can use it again for another day.

Example:

If a ticket (Tarrytown to Yankee's) was punched once leaving Yankee's E153rd St station but not collected on the train (due to crowding, etc), you can't use it again to get on at Tarrytown to go back another day. The same thing goes for someone boarding at Yankee's when there is no game and a ticket with one punch is presented. Although I have heard some creative excuses when this does happen.

Willets Point has the same policy on Mets game days and during the U.S. Open.

I did this the other day:

Purchased a Bridgeport-Yankees one way ticket since I went to the game last Friday night. Coming home, it got gate checked for 1 punch, but since I took the direct train home there was no second punching on the ticket, but it made it useless since it had already been punched once at the gate. As soon as I got off the train in Bridgeport I threw it in the trash.

Thanks for your answers - consider my curiosity quenched. :D

Part of me was sure they had some sort of contingency for these things, part of me to be honest was unsure, and another part of me was just curious as to how it worked, and now my Qs have As to go with them. Thanks again. :D