Yes, such a site can be created without infringing copyright
Facts about the game are facts.They are not protected by copyright. Criticism of, and comment about the game, is an activity protected by the US First Amendment. Making such comments is very likely to be fair use under US copyright law.
In general the author of a work, such as a book or a game, or the maker of a product, has no right to grant or withhold permission to discuss or comment on the work. This is true not only under US law, but also in the law of most countries (perhaps of all countries).
The name of the game might well be protected as a trademark. But that does not allow the trademark owner to prevent discussion of the game, clearly identified by the name of of the game. As long as nothing is being sold or rented, or advertised for sale or rental under that name, and there is no attempt to claim that the site is sponsored or approved by the trademark owner, and there is no likelihood of confusion, there is no trademark infringement. This is true under US law, and under the trademark laws of most other countries.
A wiki is a specific technology. It can be used for community discussion, or for a company's internal documentation, or for any of many other purposes. Wikipedia has popularized this technology. Not all community discussion sites are wikis, however, nor are all wikis for community discussion. Just as not all novels are books printed on paper, and not all books are novels.
In any case, setting up a wiki about a topic such as a game, a movie, or a novel does not require permission from the owner or creator of the game or of any trademarks associated with the game or work. The same would be true for a discussion forum about such a game or work that is not a wiki.
If a wiki uses excessive quotes from game dialog, or uses the game's logo without permission, or reproduces other game assets, such as character art, maps, and the like without permission, that might be copyright infringement.