You would do the same in a civil law country, sue the sports league and ISP. State that an "unlawful act" happened (blocking your service) and claim damages due to loss of traffic and the extra work it caused you.

But is it actually an unlawful act? A judge decreed that La Liga can demand the blockage of certain IPs. La Liga demanded the blockage of certain IPs. Does the fact that it had an unintended consequence on others somehow make it illegal?