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Efficient Verifiable Delay Function paper suggested that there is two way to construct the group. One of them requires trusted setup in the sense whoever constructs the RSA unknown group order needs to destroy the factors otherwise fake proof can be constructed.

Another way is using a class group of imaginary quadratic fields. However, the paper didn't give an example of how it can be used. Is everything else except this step the same, or it requires different proof verification?

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The paper actually explains how to sample parameters for the class group setting on page 9. Everything else is oblivious of the particular choice of the hidden order group. The description given in the paper is not specific to RSA groups and can be instantiated identically in the class group setting.

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