Filing a dispute with American Express is a good move - they'll take a look and if it's unreasonable AmEx usually sides with the customer. If you don't have it already, I'd also ask for a copy of your registration card - that'll prove what you signed and may state what is considered a valid reason for keeping part or all of the deposit.

What kind of damage are they claiming was done to the chair? I've never even thought of worrying about little dings and scratches in the room - all of that would fall under normal wear and tear in my view. I've always viewed the deposit as there to cover theft (e.g. stealing towels or bedding from the room,) blatant disregard for hotel policies (e.g. smoking in a non-smoking room,) or extreme damage to the room (e.g. ripping out a drawer and obliterating it - something that's obviously intentional or extremely reckless.) If someone's running a hotel, they need to understand that wear and tear is expected - and 10 months is enough for a chair to show that if they went cheap (which, if they're charging a customer for what sounds like minor damage to a chair, they probably did.)

I don't think you'll find many hotels that will walk up to the room and document every little ding with you - there's simply not enough staff to do that, and the vast majority of hotels don't care because they're reasonable and understand wear and tear happens in hotel rooms. I'd wait for American Express to rule and determine what happened.