Vector forces and leverage, that board is not holding your weight, the leverage against it is something like 10x your dynamic mass, which is higher than your actual weight. "should" wouldn't be something good enough. The alternate option, a stopper knot pinched between the door jamb and the door is also placing a lot of strain on parts that are not really strong, but most of it is in compression, not flexion (although there would be some in a weak doorframe). There is probably more meat at the window sill than there is at the bedroom door frame in most north American houses. External windows are not usual redone in renovations, but internal walls and interior doors in old buildings are very often held in with spit and hope, especially in rental properties. So unless I could verify a steel door frame (and even then, there is no way to verify if it was bolted down correctly).
The ideal anchor is directly in line with the decent, the next best is a way over built anchor as close to the line of decent as possible, but in an average house the best you would get is the base of a doorframe, which while it would be the strongest, would be the worst angle for the anchor.
Short version, know your structure, don't half ass it, if you are going to end up just falling, you are better off with a short "arm hang and drop" with a "paratrooper landing" than trying to attempt a poorly planned rapelle which more likely leaves you falling on the back of your head (unless you just want to make it less painful, and then in that case, just straight dive out the window and eat pavement like you mean it.) Not to be dark about it, but either you are in a building big enough that the fire stairs are a safe exit, or you are in a small enough building that a straight drop is an injury but survivable. As a joke a buddy and myself figured out how I could rope exit my 8th story apartment, with my wife from a dead sleep, when I did rope work every day, and in that case I stood a chance for a 7-minute exit if I had most of the rig ready at all times. That was a worst case, since the building was concrete, so the walk to the bottom would have been easier, but it was an interesting mental exercise. I could do it, with every advantage. Could I do that today? Hell no. There are buildings that are wood frame that are more than three stories, and in that case, yeah, maybe it's worth having a window exit, but you can get some very solid steel hooks fabricated, and a good folding ladder (hard rungs, rope runners) for a few hundred bucks. Well less than what I've got invested in rope gear, training and time. So if someone was actually facing that as a concern (fun fact more than a couple of suburbs of Calgary are exactly that type of building) You want an exit that tired you, sore you, injured you, your drunk buddy couch surfing, and the other people on your floor freaking out can use, not some hero "lone survivor" bullshit.
It's a fun mental exercise, but as soon as you recognize that you are not a sociopath, you realize that you better be helping your elderly neighbor down the fire stairs or you will have a really hard regret to live with.
I'm good. I don't live in an apartment building these days. I should definitely do some rope climbing though. I read a quote once that went something like "every man should be fit enough to be able to save his own life in an emergency". To me that means being able to lift your own weight up and over things, or just being able to run well. The running part I have down pretty good. If it ever came down to being able to run away from danger, then I've got that covered! 