How is your credit score affected if a credit card company closes your account because of inactivity?

Your credit score is affected by ALL the information in your credit history. Specifically, a recently closed, inactive, revolving account would impact the amount of credit available to you, thus changing your debt-to-available-credit ratio. If this particular acccount was the oldest account in your file, closing it would also shorten the history of your open credit accounts. The amount of impact to your current score would depend upon what remained open in your file and, once again, ALL the data showing, not just this one account.