Hi Odinnson, welcome!
Had to smile when I read "modern OS9 machine" :-) ... you know it's 20+ years since OS9 was introduced? Boy, time sure flies by!
Regarding your question - Yes and no. A lot of games will work fine in OS9 too. It all depends on how well the programmers adhered to Apple's standards. If by Monopoly you mean the mid 90s CD-ROM, yes, it will work. (there had been plenty of Monopoly games for the Mac)
Now SSI games are another matter. Their sloppy Mac ports were often disappointing "DOSish" and I know that Panzer General / Allied General do not work. Forgotten Realms: Unlimited Adventures does work, i had that briefly running at one point. About the others - no idea, sorry. If all you want is playing SSI games on a Mac, you might be better off getting a cheap Mac LC III.