By that definition the whole of Western Europe would be a socialist state. Government services like these do not equal socialism.
I live in The Netherlands, a pretty liberal kingdom with excellent social security and unemployment benefits. But don't be mistaken, it's not a socialist country. Not by a long shot. The biggest political parties are liberal-conservative and social-democrats. The latter lean towards the left, but our only true socialist party is much more to the left. They're only the sixth party by size.
It's endlessly bizarre to see Americans throw around the word "socialist" as if it was a curse. Western Europe is made of social democracies. Northern Europe in particular has made the choice to live with high taxes and better social services. It does not mean that they are governed by unelected oligarchs, they get the same kind of elected oligarchs as the rest.
There has been a concerted campaign in the US to convince people that other countries' social services are inefficient, dangerous, and hated by their populations.
Most of the Western Europe is ruled by Social Democrats or Socialists of various kinds. While it might be less pronounced in Netherlands or Germany, you could take a look at Denmark, or Sweden, or France, or find out what were the slogans of the latest campaigns in Spain.
According to the dictionary definition of socialism, it requires 'socialization of means of means of production' or 'social ownership'. In the current crop of Western Socialism, this is done via governmental regulations of business and large redistribution of wealth via taxes.
Note that Socialism is not Communism. It can rather well coexist with a market economy, as long as both are somehow constrained, and the economy is strong enough (like in Germany or France, unlike in Spain).
"Government services like these do not equal socialism."
So why is it socialism for the government to use tax money hire doctors and nurses to help people (e.g. UK NHS which was very clearly seen by its founders as a socialist endeavour) and not socialist for the government to hire soldiers to defend the country from attack?
NB I'm from the UK where it's clear that the public sector here has some of the very best people working for it (in the front lines of the NHS and the military) as well as some of the worst (particularly senior leadership in both organisations).
"A political and economic theory of social organization that advocates that the means of production, distribution and exchange should be owned or regulated by the community as a whole".
Most countries are like that, the US and European countries included: those countries own the means of exchange (they decree the fiat money they own as the only legal currency) and they regulate the means of production and distribution (exacting taxes and benefiting cronies).
Moreover, what those countries have is definitely not Capitalism, because capital comes from savings and most (all?) of those countries have a trade deficit (even major exporters) which means whatever game it seems to be they're playing amongst each other isn't the usual praxeological capitalism where both parties profit from a trade. Right now they're playing a game called QE, with Japan winning (which means, losing).
I live in The Netherlands, a pretty liberal kingdom with excellent social security and unemployment benefits. But don't be mistaken, it's not a socialist country. Not by a long shot. The biggest political parties are liberal-conservative and social-democrats. The latter lean towards the left, but our only true socialist party is much more to the left. They're only the sixth party by size.