When you are destructuring an Object,
you need to use the same variable names as the keys in the object. Only then you will get one to one correspondence and the values will be destructured properly.
and you need to wrap the entire assignment in parenthesis if you are not using declaration statement, otherwise the object literal in the left hand side expression would be considered as a block and you will get syntax error.
So your fixed code would look like this
'use strict';
let cat, dog, mouse;
let obj = {cat: 'meow', dog: 'woof', mouse: 'squeak'};
({cat, dog, mouse} = obj); // Note the `()` around
which is equivalent to
'use strict';
let obj = {cat: 'meow', dog: 'woof', mouse: 'squeak'};
let {cat, dog, mouse} = obj;