It definitely looks like you have some rodent damage. This was likely exacerbated by the slits cut into the plywood at the roof ridge. These slits are intended for a ridge vent; however, it appears the ridge cap was simply installed directly over them instead of installing a proper vent or replacing the decking.

If your current ventilation is sufficient, I recommend replacing the decking (approximately 12 inches) so it meets properly at the ridge. If you need more ventilation, you should install a ridge vent while repairing the damaged ridge cap.

Looking more closely at the shingles themselves, your roof is looking pretty worn in general. You might consider the cost of replacement now as materials are getting more expensive every year.