The big philosophical matter at issue is whether the Sherman Anti-Trust Act applies to a case in which one corporate entity exercises a monopoly on the marketplace of presidential debates; also, whether the presidential campaign in its current form embodies commerce. The bigger, darker matter behind and amid that issue is whether our entire electoral process can be construed as a network of business transactions.
Keep in mind that this lawsuit was originally filed in September 2015, attempting to pressure the CPD into dropping its arbitrary criteria for appearance in the televised debates. Per the wiki:
In 2012, Libertarian presidential candidate Gary Johnson filed an anti-trust lawsuit against the CPD, the Republican National Committee and the Democratic National Committee in D.C. Circuit Court citing the Sherman Act and claiming "restraint of trade" for denying competition to, for example, potentially receive the $400,000 annual presidential salary. The case was dismissed in 2014 due to lack of jurisdiction.
In September 2015, the Libertarian and Green parties – along with Johnson and Jill Stein – filed another lawsuit against the CPD, the Democratic National Committee, the Republican National Committee, Barack Obama, and Mitt Romney, charging violation of federal anti-trust laws. The case was dismissed in August 2016.
Confession: I haven't read the brief all the way through, but I plan to very soon.