Yes, this app supports multi-select picklist fields as well, see the below screenshots where we have added the multi- picklist field on the Client Update Details Form.
On Client Form -
On the Approval Page -
P.S. Discover Update Client Details, the easy way to keep client information up to date in Salesforce. Find it on AppExchange - https://appexchange.salesforce.com/appxListingDetail?listingId=a0N3A00000EcsATUAZ