Technically it would negate the status of "legal tender" to the money, not really something that a state or governement can allow, not even in private transactions, but of course the article is largely exaggerating:

Title: ... cash is on the verge of extinction...

Inside:"Electronic payments in the Netherlands’ shops and supermarkets overtook cash payments for the first time in 2015 by a narrow margin: 50% debit cards while 49.5% were paid for in cash the remaining 0.5% were credit card-payments. There’s a movement afoot by a coalition of Dutch banks and retailers that want that ratio to increase to 60% electronic payment versus 40% hard currency by 2018. "

So not on the verge extinction at all. Also, whenever someone brings up the a northern European country as the trendsetter for the rest of the world, I can't help but be skeptical.

Where laws exist they tend to be worded around debts only. A store is free to demand payment by any means they wish.

And I am free to not buy from a store that does not accept cash.