"Party", as defined, is another manipulation. Similar to the way the US Trade Representative nominally represents the interests of the USA, while really representing the interests of legacy corporate power, so too the Parties, at least on the side of the party raising the objection under the agreement, represents corporate/investor interests.
If you don't understand the context of these documents then you can't really know what powers they provide to the different parties (in that it doesn't outline what powers the different parties current have under the existing trade agreements and international/national law and how those would change). The point is that no nation is going to sue another nation for their environmental laws. Foreign investors who see an opportunity for profit however, will, and do, sue on a regular basis. Right now a US company is suing Quebec for environmental laws that prohibit fracking. But they have to sue in Canadian courts, which, at least to some extent, gives the home country advantage to the defense. With this agreement investors will no longer have to sue in national courts, but will use these arbitration panels instead. Given that close to 100% of the suits brought before these panels will be by investors/corporations against foreign nations, the reason for the panel selection bias becomes apparent.
And if this leads you to realize that this agreement, if approved, means foreign corporations have more rights that domestic ones, you'd be correct.