looks like this is outdated as it still uses classes

This Kata is completely incorrect. If you think React then you can't solve it.

I think this kata's test cases are incomplete.

For my submitted (incorrect) solution, I've actually just submitted the beast value input by the test case in the beginning. The form input element's value is not used.

In a practical world where humans are inputing the form, I would have to read the form input value, then submit and run the requested function using that value.
The test cases did not use the input element to input value, hence I found my "wrong" solution accepted just using the test-case-injected value.

Also, please update to >= React v16.4.x

There is React.createRef already. Kinda confusing when following the current (v16.11.x) documentation, but the React.createRef returns error upon testing.

It maybe worth adding an assert to check Beast.defaultProps is set with name: 'Yeti' to create awareness of it. Since you have used it in your solution.
As it is possible to set a default in the constructor using or operator or ternary operator. Maybe mention it in the description as well.