They want a credit card for a couple of things.
1.) It helps to ensure that the same person doesn't open new accounts every 10 days and be able to have a free paid membership indefinitely.
2.) If you decide you like the features on the paid membership, then you don't have to do anything to keep it. After 10 days, the site will charge your card automatically to continue your membership. If you don't want this to happen, you need to cancel the membership before the 10 days are up. If you miss the 10 day deadline, you should still be able to get a full refund if it is still within 30 days.
When i loged in chess.com today first thing i saw was an offer from chess.com free trial membership for next 10 days, when i accepted it sais ,,Oops?! We noticed the following errors in your form:
Card Number is required: So is it free or not fgs?!! If it is than why do you need my card number?