According to Grammar.yourdictionary.com, the name of the game should stand out from the rest of the text; so, you can either put underline or you can put the name of the game in italics_.
Italics are used for large works, names of vehicles, and movie and television show titles
Italics are used in the titles of:
Books; Full-length plays; Long poems; Music albums; Anything that has sections, like anthologies or collections; Newspapers; Magazines; Movies; Television and radio shows; Ships (With ships and other craft, the USS or the HMS is not italicized); Airplanes; Spacecrafts; Trains; Some scientific names; Court cases; Works of art; Musical works like operas and musicals; and Computer and video games
Of course, italicizing is easy on the computer, but what about if you are hand writing something? In such cases, underlining is still used and is the same as writing a title in italics. However, you should not both italicize and underline a title.
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