Altough I am not an expert in Time Relativity like Albert E., I cannot call "present time" something that will happen "after" this very moment. What is going to happen in a very near future has not happened yet. So the baby is crying now and won't stop crying until some future moment (hopefuly in a very near future). What we are willing to do, can we say that we are already doing it?
Eh... erm... ahem.... that page 'shows' that it can imply future tense. It does not, however, 'show' that it always implies future tense.
A key factor to remember about 'will' is that when we talk about the future we cannot always use 'will' and that when we use 'will' we are not always talking about the future
However, in these examples 'will' is referring to events happening at the present. • My car won't start.
You couldn't possibly think that "My baby won't stop crying." is implying the future tense.
There is a difference between "The door does not close" and "The door is not closed".
A porta não fecha = the door does not close (close is a verb showing the action the door makes)
A porta não está fechada = The door is not closed (closed is an adjective describing the condition of the door)
It works the same with 'shut', only 'shut' is even more confusing because the same word can be the verb or the adjective, without changing form like 'close' and 'closed'