This is definitely an FP vs OO thing. If you wanted to refer to the value in an ADT you'd introduce a new type to refer to it, which in Elm would be:
type Message
= IncrementBy Amount
| DecrementBy Amount
| Set Amount
type Amount = Amount Int
Obviously this is a contrived example - you wouldn't bother if you were dealing with an Int but once the message gets more complicated it can make sense.