It's helpful in web development, it allows you to target specific browser versions. For example if I use a new feature on my website which is only supported by recent browser versions, I can inform the user about the incompatibility and prevent complains.
I also don't think Google needs that info, there's a million things to criticize them for but this is a bit silly.
Feature detection is more reliable than version checking, as it can more correctly support a wider range of browsers (that you didn't think to version-test for). There might be some cases where that's tricky, but it's generally straightforward. Tools like https://modernizr.com/ can help with that.
I also don't think Google needs that info, there's a million things to criticize them for but this is a bit silly.