The chain’s not going to admit anything is their fault as a matter of policy. If they forgot to put the oil in and the engine seized two minutes after you left the shop, they would still deny everything.
Did they cause the damage by adding too much oil? Your best bet is to ask the manufacturer. There is a warning on the dipstick. The manufacturer must have had a reason to add this warning.
The facts are, you went to a chain for an oil change, they overfilled your oil against the manufacturer’s warning (and admitted it), and the engine suffered damaged within 200 miles of the oil change. How do you think this is going to look to a small claim’s court judge?
Sue them in small claims court for the cost of repairs. Watch a few Judge Judy’s before you go.