Well this has been instructive. Like Umbran, I am a bit surprised to see as many people being upset by this advice. Not so much that some people are upset -- that's a given -- but the degree of upsetness, and some of the authors of the upsetness have been surprising.
It's been a bit odd. People who are often quite rational suggesting that professional writers copy and paste from other documents; attempts to say that "consent" should be confined only to sexual situations. The believe that any statements intended to encourage safety are, by their mere existence, making roleplaying appear unsafe.
I expect people to say "I don't need to do this because it's never been a problem for me" -- that's a common statement made to any suggestion that requires change. I expect people to say "I don't allow the pain of one person to take priority over the fun of others" because that's just lack of empathy that you can see everyday, and I also understand people saying "I don't see why we need this, isn't it just common sense" because, yes, it would be wonderful if that were true!
I direct plays and musicals. One of the things I say upfront is something on the lines of "The goal is for everyone to enjoy themselves. As a director, I will try to make sure that happens, but if something is causing this not to be fun for you, let me know. If I am using the wrong name for you, or the wrong pronoun, let me know. If you don't feel comfortable talking to me, talk to <X> or <Y>. As an example, I don't like to be called 'a brit' -- it's not a bad word, or wrong -- it just annoys me, so don't feel it has to be something big to ask for a change."
I didn't used to add this to my usual speech, but it was reading and listening to messages very much like the document which we are discussing that made me realize I need to. If, as a GM or a director, I do not explicitly tell people -- using words, a checklist, or anything -- that they have my enthusiastic permission to make discomfort known, then they will very likely assume that the default position is, as several have stated on this thread: man up, or move on.
I believe I am a good GM and a good director, and so I believe that if someone says something is a problem, then I can fix things so that the fun of the group (or audience) is not compromised AND the pain it causes the person is avoided. It's not an either-or situation. I do not believe that if spiders are found to unexpectedly cause someone strong discomfort, that I cannot work around it.
So, if I can solve the problem without compromising fun for all, this seems a no-brainer -- why wouldn't I do it all the time? And if I can solve it all the time, why wouldn't I use a tool such as this document, a checklist, an X card or whatever so that I can realize the problem exists and fix it?
If you honestly do not believe that you have the skills to fix a consent problem, then the up-front checklist becomes an even more important tool for you, to avoid putting yourself in a bad position where you have to choose either to hurt someone, or make the game less fun. But I am optimistic that the people in this group are able to solve situations like this, so it makes it puzzling to me that they would want those situations to remain invisible to them.
I'm going to suggest that if you have an instinctive reaction against the document, maybe don't think of it as a way for someone else to police your game, but instead think of it as a way to make sure that your players know that you are a GM who welcomes the task of making everyone comfortable at your table and has the skills and the will to make that happen.