We have games too. We do always open them up to see if they’ve been used and if they have, we “re-set” them (the pieces, manual, etc how they came originally) so that they look appealing and tidy to the next guest. We can tell if they’ve been used because no one else puts everything back like that - so that’s one way you could tell. Or you could just ask them to leave out anything they use.
People who aren’t worried about it will enjoy and appreciate the games. People who are worried about it just won’t use the games.
Even though I am learning that we apparently clean much deeper than most hosts, we don’t sanitize every scrabble piece and still won’t (though we have cleaned pieces that were clearly used while eating pizza, lol). We also have bookshelves with lots of books and we don’t sanitize each book either (but also wipe down obvious handling). However, we are also going to leave 3 days between guests and that is sufficient for books and such to not be infectious to the next guest. (I know not everyone can do the 3 days but we’ve been enjoying the break from constant back to back guests and have decided to give ourselves that extra time).
For reference, I’m not lackadaisical about cleaning. We have medicine cabinets and shower caddies stocked full of amenities in the bathrooms and we have always wiped down every single one between guests. Likewise in the kitchen, we provide numerous canisters of teas, coffees, etc and all kinds of oils, vinegars, etc and we have always wiped down every single container in between guests. There are lots of things to spread before covid, like norovirus, MRSA, e coli, salmonella, flus, colds, etc. I don’t think anything should be provided in a kitchen or bathroom that doesn’t get cleaned between guests (with or without covid).