To speak generally, discourse gaming is the practice of trying to persuade people in ways that don't involve appealing to their discretion and judgment. The theory is that you can get people to think about things in a certain way - or make them more likely to think about things in a certain way - without their active intellectual consent. Contrast this with another style of communication, where you simply present information to people as clearly as possible and accept that they're going to interpret it and evaluate it in ways that you can't necessarily control.
Some important caveats.
First, obviously, all kinds of things influence discourse. It isn't just some cut-and-dry process of exchanging and then actively, rationally evaluating information. On the contrary, discourse can be influenced by factors as minute and remote as how much sleep one had the night before, whether the speaker's tone of voice reminds one of one's mother, the personal associations one has with certain turns of phrase, etcetera etcetera.
Second, it's clear that we do have some ability to manipulate the things that influence discourse - to game the discourse, that is - in predictable and consequential ways. This is the scientific basis of all kinds of productive and important fields like marketing, public relations, and even psychotherapy.
When I object (and ridicule) discourse gaming, as I so often do, it's always for the same reasons. Usually, it's because people have absolutely unrealistic ambitions about what they think they can accomplish with discourse gaming. A great example is the guy from The Hill who thought that he would be able to manipulate Sanders supporters into backing Clinton by covering him favorably during the primaries and then backing her in the general. This is not completely crazy - people are usually more persuadable by voices they trust than by voices they have a combative relationship with. But here, the theory seemed to be that a few kind words about Bernie from an obscure journalist would somehow build enough affinity with readers to overcome the deep and powerful material / cultural forces pushing Sanders voters away from Clinton. That is completely ridiculous, insulting to the intelligence of his readers, and betrays a certain hubris about the extent of his influence.
If (say) this guy were to kidnap a Sanders supporter and spend several consecutive months ego-stripping him and engineering a deeply co-dependent relationship, perhaps the resulting emotional / psychological investment might be enough to overcome the victim's political sensibilities - but short of something along those lines, it's just extremely unlikely The Hill guy's plan would work, and the far more probable outcome is that Sanders supporters would simply start disagreeing with him once he pivoted towards Clinton.
In general, the sort of extra-rational dynamics that can consequentially influence discourse are often extremely hard to implement; the target has to be completely and constantly immersed in the new discourse environment, not just sporadically exposed to some clever trick of rhetorical framing or sloganeering.