That can be a bit of a tough call, speaking as a landlord myself. If the lease or house rules required floor or carpet protectors under wheeled chairs then it's pretty clear that it's not wear and tear. Merely asking the tenant to do it that way probably won't qualify as "house rules" and certainly isn't part of the lease. At the very least, you should have notified the tenant in writing to use a proper floor protector under all wheeled chairs.

My leases always required "appropriate" carpet protectors under wheeled chairs used on carpeted surfaces but never on hard floors. I did have one tenant who disregarded that and did bill him for the replacement carpet.

A properly installed hardwood floor -- and you'd be surprised how many are NOT properly installed -- should not suffer significantly from that type of traffic. (My Dad had his office in the home and had 6 or 7 wheeled office chairs in use for over 20 years and never did any damage aside from the occasional scratch on the hardwood floors.) If it's not properly installed, of course your tenant isn't responsible either. Or if it's a cheap composite or laminate with a thin wear layer, again it's probably not the tenant's responsibility.

My best advice would be to have it checked by an experienced flooring installer and get his opinion. You're going to have to have a pro fix it anyway, so that's not any additional cost one way or another. If it's his opinion that a reasonable person would or should expect that sort of damage under those conditions, ask the tenant to pay or offer to split the cost. If not, then you'll have to eat the cost yourself. And maybe consider modifying your lease terms or publish appropriate "house rules" and give copies to your future tenants.