This is relevant to any startup. Yes, brain cancer is an extreme case, but just as it's important to select the right cofounder, having something unexpected or unplanned happen to your cofounder is a situation that has to be handled.
It could be something as awful as brain cancer[1], as joyous as a new baby or as horrifying as discovering that the new baby has a hole in his heart, or something that is both positive and negative, such as falling in love with someone who wants or needs to move away from your business location.
Key man insurance can help, but notes on experiences such as this are helpful as well. It's easy to pile onto the author as an insensitive schmuck because you are not in that position. We can't directly relate to his situation, so we can judge all we like without fear of hypocrisy.
However, at some point, if you are lucky enough to grow a company and you are responsible for the livelihood of your employees, a key member of the team will have an 'availability-limiting event' that will force you to make tough decisions.
Having articles such as this help. Not all the advice is immediately useful ("hire a bunch of interns") but dropping meetings and intensifying focus is good. Keeping in mind,"How should I handle this so that I don't leave this in a mess for X?" is good as well, because it assumes that X will be back.
If this happens to you, know that you have google/duckduck/bing fodder to look for help in your moment of panic. Know that while it's one thing to think,"I have cancer and I have to figure out what to do with my startup," for which you can find a number of bits of advice, it's another to be affected as a partner. Know also that you should make sure that you cross-train enough with your cofounder so that neither of you is trying to do a brain dump to the other in the back of an ambulance while your loved ones are terrified.
Finally, I would find it hard to believe that the author posted this without his partner's consent. It sounds as if they've gotten through the immediate crisis with the tumor and he is probably at least partially re-involved with the company.[2]
Take posts such as this at face value. Have compassion.
[1] Fuck cancer.
[2] Chemo is a bastard; see: [1]