The table and first example in section 11 are misleading, but the remarks in section 9 are correct and address your question: roughly speaking, deste means of this, not just this; and desse and daquele mean of that. The first thing to know is these words are contractions of the preposition de with a pronoun:
deste = de + este [of this (near the speaker)]
desse = de + esse [of that (near the person you’re speaking to)]
daquele = de + aquele [of that (over there)]
The differences among este, esse, and aquele are addressed at length in this question. I'll focus on the role of the preposition de. The reason it looks as though deste means this in some sentences is that some Portuguese verbs need the preposition de whereas the English equivalents do not need any preposition. For instance gostar de (something) is equivalent to like (something):
Eu gosto de vinho = I like wine
Este vinho é bom = this wine is good
Eu gosto deste vinho = I like this wine
In the last example it looks as though deste means this, but it does not: it means of this, except the verb like does not take any preposition, whereas gostar takes de. The site’s second example is correct: to ask for someone’s opinion on something you can use think of (something) and achar de (something):
O que voçê acha deste vinho? = what do you think of this wine?
Acho que este vinho é muito bom = I think this wine is very good