Least I Could Do can not give the characters in-depth personalities because it's a short gag comic. To complain that a comic with a focus on chracters and story has shit characters is more valid. Same thing with misogyny. If it's blatant and pervasive enough for you to be legimately annoyed by it then complain about it.
By that argument, Sinfest could also not be accused of misandry because it's a short gag comic. Of course, Sinfest is a blazing example of misandry, just as LICD's deeply ingrained misogyny is obvious to pretty much everyone except you.
The author of the LICD review clearly thought the comic's baked-in hatred and contempt towards women was "blatant and pervasive enough" to be "legitimately annoyed" by it. You don't, and you've tried to make your case as to why, but I don't think you've made a very compelling argument. What you've just suggested is that misogyny somehow requires a story where characters have in-depth development, which is arbitrary and unsupportable.
Never said that a gag comic can't misogynistic. What I said that is that it doesn't matter. From what I've seen of LICD, it's all sexually based and the punchline is not really at the expense of the woman. Objectification and stereotypes and what have you really don't matter if you're working in a couple of panels .LICD is pretty indirect with it and you’d have to be going out of your way to make a case, honestly, those are probably the least offensive forms of misogyny or any kind discrimination. Shadbase is closer to being “blatant and pervasive” but it’s pretty indiscriminate so again, it’s kind of moot to mention. Misogyny doesn't require a complex story to be considered misogyny but it makes your offense (and complaints) a lot more valid in my eyes.