I can somewhat replicate the issue you describe. It does not appear to be "some other random voice," but rather when you select a voice in Chess app > Settings, the actual voice used is the option directly above the one you selected, and only if the selection is below Samantha (English (US)).
For example, when selecting Zarvox as you show for your primary voice in the screenshot, the voice used by the Chess app is Yuna. Similarly, if I select Zosia, the voice is Zarvox.

For me, this issue only affects voices below Samantha (English (US)). Selecting Samantha (English (US)) gives that voice, but selecting the choice directly below that, Sandy (German (Germany)), also gives Samantha (English (US)), and all choices further down the list are offset by one. Choices above Samantha (English (US)) give the selected voice. Samantha (English (US)) is the default macOS System voice and the one selected on my Mac, so it is possible that selecting a different system voice (which the Chess app should use for the Default Voice selection at the top of the list) will change the 'break point' below which the selection is shifted.
This issue does not occur on my Mac running Tahoe, so it appears to be a bug in macOS 27 Golden Gate. Bugs should be reported to Apple here:
Feedback - macOS - Apple
Well spotted!