Yes - you have to be a member of the Chiemgauer e.V. association in order to use or accept the vouchers, which is why it's called "vereinsintern", i.e. "internal to the association". It's not a general-purpose currency.

Have to? What happens if a random business accepts them for payment, and uses them for purchases at other accepting businesses?

IANAL, but the association giving out the vouchers would probably sue for fraud, since the merchant acts like a member of the association even though they are not.

That is a very very strange thing to consider fraud! Imagine applying the same logic to someone that will trade their wares for baseball cards.