The goal is not clear to me, either. If Pence has the sole authority to accept or reject the electoral certifications, then how can a court force him to exercise his discretion in a way that will aid the President? While I believe the President won the election, I would be surprised if any court intervened to tell Pence how to exercise his authority.
From reading the wiki article - the act effectively takes the count out of the VP’s hands and the governors of each state have final authority over which electors from the state qualify in the event of a tie and both houses of congress can override the VP if they have the votes.
My comment above is in agreement. Moreover a court cannot intervene until he has exercised the discretion of his office or refused to do so.