The Railcard website you linked is pretty clear.
> For those aged 16-25, save 1/3 off rail fares for days out, seeing family and friends and even festivals!
> For those aged 60 and over, save 1/3 off rail fares for days out, holidays, seeing family and friends, and theatre trips!
So, provide proof of age via ID and get a discount. It's very common on public transit for the young and elderly to get a discount.
Proper ZK off of that would be it would simply provide which of those age ranges you're in, not your actual date of birth.
and the 26-30 Railcard, and the Children aged 5 to 15, and the for those aged 16 or 17, it just seems weird to have all these age-restricted options for exactly the same product (a seat on a train.)