I googled a bit, and perhaps this statement comes from this old Reddit thread here in the first comments.

There it’s mainly used as a joke to describe how Windows is just very backwards compatible in general. The story might have stuck and warped a bit as like it really had a reference to that Barbie game.

I know there was an old hack for simcity but I’ve never heard about barbie. I’ve checked and the claim seems to come from (now removed) @pwnallthethings twitter account. What he refers to there is that Windows indeed maintains a compatibility database, which, unlike the normal compatibility menu, allows more compatibility tweaks and works entirely automatically. On my fresh win11 install, the compatibility administrator tool lists a few hundred compatibility shims and thousands of apps listed, with “Barbie Adventure Riding Club” indeed being one of them