Much of this is a result of the way health insurance and spending is classified, with only 35% paid for by government in Switzerland rather than 80% in most other EU countries and 55% in the US.
Adjust for that and government spending would be around 39%, still low for a rich European country, but not so far off of somewhere like the Netherlands or UK (about 44%).
Sure, but there are private aspects to the system and if we are going to list everything that is strongly regulated by the government you likely get to a higher number. The Dutch, as far as I know, but not sure, also have some kind of private insurance system, so might get hard to compare.
Healthcare is such a large part of national expenditure that I think it is worth adjusting for it when comparing government expenditure shares of GDP. It is around 12% in Switzerland.
Many countries organise healthcare largely through non-government health insurers, but those still get counted as part of government expenditure in both Netherlands (69%) and Germany (80%), not much less than the UK's (83%) with a National Health Service. Switzerland on 35% is a huge outlier here.
In terms of administration the Swiss system seems not completely dissimilar to the German system in that coverage is mandatory and there are a range of non-profit providers to choose between. But the Swiss scheme is classified as private expenditure because its mandatory payments are made directly with income based subsidies rather than equivalent amounts being paid through the tax system.
That one simple accounting change lowers the government share of GDP by 5.4%.
Adjust for that and government spending would be around 39%, still low for a rich European country, but not so far off of somewhere like the Netherlands or UK (about 44%).