score:4
To be honest, it doesn't look like a very well made booking service and they probably have no online payment procedure in place.
Even when you go to make a booking, at the end where you are presented to agree with the "terms of services", if you click "read terms of service" it's a blank document saying "these are the terms of service"...
Call them up and explain your concern about there being no card reservation and I'm sure you'll have your answer. The hotel seems very busy this time of year, they probably aren't that bothered if someone cancelled the day before, and they may even be hopeful of cash payment on arrival or charge more for a card (if places still even do that).
I know with small family ran places no card details are usually asked for, and for big chains they can allow cancellation same day upto 1pm.
They are on booking.com and are part of a hotel group, so if they confirm the booking you should be fine - just call them about the lack of a card reservation if you want to put your mind to rest.