Based on what you showed, it looks like the delay is your fault.
It says you disputed the charge the same day you signed up. (February 19th)
Do you know what that means? A dispute is an argument about something. You dispute a charge when you don't think you should pay.
I don't know what happens in India, but in America, the bank will contact the merchant and the consumer to see what happened. That can take a while.
You should write an email to support. Be sure to use the billing dropdown and tell them that you want the membership. https://support.chess.com/customer/portal/emails/new
You might have to make reference to this thread since I don't think you can attach anything when you use the contact form.
Sir, Im Zamte hrahsel saza , i had paid a Platinum Membership fee of chess.comfor 1 month Rs 492.36 .Payment also success but it not work till today.What should i do ? Please help me.