In the sentence: Some of these games are similar to Hollywood Squares, Jeopardy, Payday, Life, Monopoly, UNO, and play money. Okay, Hollywood Squares and Jeopardy would be italicized since they are TV shows. Would board games (such as Monopoly) and card games (UNO) be italicized? I did a search on CMOS and found nothing. Thanks.
I remember reading somewhere that board games aren't italicized. They're left as they are. However, since no style guide really comments on this (I believe the AP manual talks about how to cite games as references, but that's it), it might just be a stylistic issue. Maybe someone else can give a more definitive answer.
I would guess the same rule as for other trademarks would apply (but I don't know what that rule is, though I would not italicize).
I do not believe that TV shows should be italicized, but rather placed in quotes: "Hollywood Squares". Same with board games. But, as in all similar matters, I defer to @mammamaia.
If there are no hard and fast rules then I guess it's a style issue and it's up to you to choose, just make sure that you do the same for all of them throughout the text. Personally, I would only put it in italics if it were mentioned out of dialogue.
i see no valid reason to write board games' names in any way other than as they appear on the game itself, as they are trademarked objects akin to Kleenex and Twinkies... however, since games shows on tv are just another tv show, their 'names' are thus'titles' and should be written following the rules for titles, which call for different treatment of the title and the episode, the same as is done with magazines and the articles contained therein... i follow s&w on this issue and recommend doing so... though, as in re all styling issues, each publisher's house style/preference should take precedence... for backup of my styling choices, i also use harry shaw's 'punctuate it right!' guide [a real book], as well as the ones i've listed in my stickied resources thread: https://www.writingforums.org/threads/writing-basics-reference-sites.21049/