This is a good example of finding the "direct objects" and "indirect objects" of sentences. In the 1st sentence, the focus is on the three people (direct object is the three people). In the 2nd sentence, the focus is more on the room itself. (direct object is the room).

In any sentence when you have "there, here, those, this..etc, you are giving some sense of location, which the second sentence does not. "This room has three people." The circumstance you would use that sentence would most likely be when you are referring to a specific room right next to you. Like another example would be, let say a cup of coffee is in front you on the table. If you said: "This coffee is hot". I would automatically assume you are talking about that specific cup of coffee right in front of you, which you are drinking. But normally even if you just said: "Coffee is hot." I would probably know what you are talking about it anyways, but having that "this" in there gives more sense of which object you are specifically targeting. Equivalent to 那里，这里， etc.. in Chinese.

I think saying "Three people are in the room," gives more emphasis on the existence of the three people. Saying "There are three people in the room," makes it sound very factual, yet bland. Anyway, they do mean the same. It is gramatically correct to say, "This room has three people." but I found it more awkward than the two sentences above. Probably because the emphasis of the sentence is on the room than on the people, and usually this sentence construction is used when we refer to the inanimate things inside the room.

1 and 2 are both okay and I can't think of any reason you would say one vs the other. This room has three people can be used if you want to specify between different rooms. This room has 3 people and that room has only 1 person.