Unfortunately you're unlikely to find a "regular" fix for this. I think Cyan is very unlikely to develop a patch for an old game. Especially considering there are full working versions available. All we have are workarounds, which are common on older games.
I'm unsure whether this is a game bug or a OS bug. I think it might simply be a resolution issue, as when Riven was designed HD displays just didn't exist. I think the most common resolution at the time was 640x480. More expensive monitors probably maxed out at 800x600. You current 1920x1080 or higher is really different.
As for Syberia, believe it or not, that actually came out 5 years after Riven did, which is an eternity when talking about computers, so it is far more likely to work on today's systems.
Right now your options are pretty clear. (1) Try using ScummVM (free). I've heard people have good results with this. (2) Get the GOG or Steam version (about $10). I know this works because this is the version I am currently using. (3) Either get an old computer or use a virtual machine with an old version of Windows on it. (potentially free if you have an older version of Windows laying around)
I wish I could be more help, but as I don't have the 10th anniversary edition (just the original 5 disc version!), or a computer running Win7, there's not much more I can do.