Question 1: Since "see" means "to understand" and "to imagine" in sentences 1) and 2) respectively, can I replace it with them? For example:
a) I do not understand it describing possession.
b) I just can’t imagine them winning the game.
For sentence (a), probably understand ... as would be better than just understand:
I do not understand it as describing possession.
Understand by itself, with or without a direct object, most often is similar to comprehend, rather than the sense wanted here similar to interpret as. The negation do not understand without as implies some type of confusion.
One could also add as in the original sentence 1 with see, without much changing the meaning:
I do not see it as describing possession.
Or for a rephrasing using a form of understand with meaning close to the original:
In my understanding, it does not describe possession.
Sentence (b) is fine, and conveys approximately the same meaning as the original sentence 2 with see. The substitution of imagine might make it a bit more emphatic, or represent a prediction that their chances of winning are even smaller.
Question 2: Do the participles "describing" and "winning" in 1) and 2) function in the same way as the participle "playing" in the following example?
- From the window we could see the children playing in the yard.
I would say "it describing possession", "them winning the game", and "the children playing in the yard" in these sentences all have the same grammatical structure there, but it's an interesting question whether they are really noun phrases with adjectival participle, or gerunds with "subjects" in front, or should be called something else. Wikipedia has a lengthy section about this question. The way I see it (see like understand intended), the participle structure doesn't quite capture the meaning well enough: the point is not that I see the word, which (I think) describes possession; or that I see them, who might not win the game; or that we saw children, who were playing. The sentences communicate that in my understanding, the word describes possession; or I can't see that they will win; or we saw both the children and their action of playing. The object of see or its replacement is a combination of noun and verb. Often that could be expressed with a dependent clause, but in this type of grammar, it looks more like a noun (either objective or possessive) followed by a gerund, where the noun acts like a "subject" of the gerund.
Of course, the phrase understand it as describing possession is grammatically different. Here describing certainly is a gerund, acting as object of the preposition as.