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My brother in christ... Let me explain the joke so you can understand the way it doesn't rely on any notions of gender to work. For an external example, listen to Patton Oswalt tell a similar joke that also compares something trivial (his pants not fitting) to a dying soldier.

"talking like a man dying in battle": This refers to a tropy type of scene in various works of fiction where a soldier has taken what is obviously a mortal wound. But the soldier is in denial so they speak about how they'll heal from the wound and about what they'll do when they get back home...as if they won't be dying momentarily.

Okay, so then this twitter woman's husband gets sick right? And he says "I'm gonna heal up and smoke us some ribs...Just like we used to do...I'm gonna get better". The content, structure, and tone of those few sentences (if you allow your mind to get into a little bit of a relaxed and humor oriented state) is reminiscent of the way the dying soldiers in fiction often speak.

So here's where the humor comes in. The husband just has a cold! Why is he saying those things? Of course he's going to "get better". But that silly billy was talking like a dying soldier when it was just a cold!!! Isn't that a knee slapper. His problem was so small compared to the soldier's but he spoke about it in the same way! ~~Why, he's a man! He shouldn't complain when he's suffering at all! What a pussy!~~

Oh wait. She didn't say that last part. She didn't imply it. Cause that's not what the joke is about. Cause the joke isn't reliant on notions of gender roles. At best ideas about gender roles adds some salt to the flavor of the joke.

Edit: I toned it down, but I hope my sarcasm and disdain for you still comes through.