I actually got an email like from an old co-worker after I was fired. It was done much in the vein of the advice in this post. It was short, friendly, and made no pretence about staying in touch. I gave a short, friendly response and that was that. I gotta say I actually really did appreciate it, and still do. Of course, I wasn’t exactly upset about being fired so I don’t know if this counts.

Agreed. The blog post starts off fairly well, with step 1 to being a good human being, but pivots ironically at the end to a list of ways not be a human being.

It feels more like how to do the minimum possible without doing absolutely nothing.

You might have been interested in continuing the conversation if the other person didn't descend into trash-talking first. I think that's the message the author is trying to convey.

But I agree with you that "I can't continue this conversation" is probably not the best way to respond, even in that case.