It is kinda required. The DMCA requires you to implement a policy for terminating repeat copyright infringers. You aren't required to call them "strikes", but you have to keep track of who is a repeat infringer and terminate their account. You have some leeway in how you implement it, but you do need to take action against repeat infringers. As such, any infringement that doesn't get overturned will end up as a strike against you (whether it's called a strike or not).