The idea seems to be "we're having a private conversation here, so go away, man". The same thing occurs in the more recent Wondermark strip:
Notice the confusion of public online space (e.g., Facebook, or even more so, Twitter) with a private space (someone's dining room, say, from the Wondermark panel). These two things are entirely different environments with different characteristics, which is why the entire "sealioning" trope is so mendacious. What it really means is that the person employing this wants their opposite to just shut up because, reasons. It is a marker for someone (say, a radical feminist) spouting unsupported, dogmatic, negative opinions (patriarchy!) about some group (say, men) in an online space where members of that group are likely to be and will take exception and loudly disagree. Luckily, Urban Dictionary has a knockout, accurate, take-no-prisoners definition:
To express disagreement with, express skepticism of, or otherwise simply talk back to an internet social justice advocate or internet radical feminist.Ayup.
Help me! help me! These white male shitlords on the internet are sealioning me by asking me to provide evidence for my accusations! I'm being harassed and stalked because people doubt me! Please donate to my paetron and kickstarter accounts so I can buy some new shoes~whoops, I mean, so I can produce some more content about how sexist this hobby that I don't really partake in is.