I read the article and the situation is technically not the end of the world. I went to the original ruling but I can't read French or German or Italian(!). However the article says basically that the Court ruling applies only at the federal level only and that:
Switzerland’s cantons may decide whether to authorize homeschooling or to ban it outright... Currently, according to the Swiss Broadcasting Company, there are more than 1,000 children being homeschooled in Switzerland. Regulations vary widely throughout the cantons. While some require official authorization and teaching certificates for parents, others only call for notification.
In some ways this is no different from the States, where HSing laws vary greatly - in NJ you have almost no regulation (surprisingly) while MA, PA, and NY have very onerous regulations including the requirement that a local bureaucrat approve your HS Curriculum. We haven't yet had a SCOTUS ruling on HSing and, frankly, I'd prefer to keep this a State's rights issue.
If I'm charitable, this court ruling simply says the federal constitution does not guarantee a parent's right to HS but locally you can, Canton permitting. What IS troublesome is that Switzerland's federal Supreme Court relied upon international law in part of their ruling.