Firefox and Safari would probably work for the majority of features but Chrome probably exposes some browser APIs that the rest don't that might make a couple things not work.
For people who know enough to spoof a Chrome user agent, they know enough not to mind if some things break but regular consumers wouldn't know about browser compatibility topics and would blame any irregularities not on their browser but on Snapchat, which is why they choose to display this error rather than let people through.
Yea that's fair, and I totally understand when sites limit to newer (last 2-3 years) versions of browsers or limit to Chrome, Safari, and Firefox.
But to cap it at just Chrome like its 2012 when browser compatibility has come such a long way is likely unnecessary and frankly lazy on their part. I can't think of an API that they definitely would need to use that isn't in Firefox.
For people who know enough to spoof a Chrome user agent, they know enough not to mind if some things break but regular consumers wouldn't know about browser compatibility topics and would blame any irregularities not on their browser but on Snapchat, which is why they choose to display this error rather than let people through.