No, it isn't.
Socialism is public ownership/control of the means of production. No one disputes that England's NHS is socialist, and the workers do not own it.
Dictionaries do not define words, they report usage. My definition comes from the way people actually use the word:
https://www.merriam-webster.com/dictionary/socialism
any of various economic and political theories
advocating collective or governmental ownership and administration of the means of production and distribution of goods
https://en.oxforddictionaries.com/definition/us/socialism
A political and economic theory of social organization which
advocates that the means of production, distribution, and exchange should be owned or regulated by the community as a whole.
https://www.ahdictionary.com/word/search.html?q=socialism
Any of various theories or systems of social organization in which the means of producing and distributing goods
is owned collectively or by a centralized government that often plans and controls the economy.
https://www.collinsdictionary.com/dictionary/english/socialism
an economic theory or system in which the means of production, distribution, and exchange are
owned by the community collectively, usually through the state.
https://www.macmillandictionary.com/dictionary/american/socialism
a political system that aims to create a society in which everyone has equal opportunities and in which the most important industries are
owned or controlled by the whole community
https://dictionary.cambridge.org/us/dictionary/english/socialism
any economic or political system based on government ownership and control of important businesses and methods of production
https://en.wiktionary.org/w/index.php?title=socialism&rdfrom=Socialism
Any of various economic and political theories
advocating collective or governmental ownership and administration of the means of production and distribution of goods.
https://www.infoplease.com/encyclopedia/social-science/government/concepts/socialism
general term for the political and economic theory that advocates a
system of collective or government ownership and management of the means of production and distribution of goods.
https://www.dictionary.com/browse/socialism
a theory or system of social organization that advocates the vesting of the ownership and control of the means of production and distribution, of capital, land, etc.,
in the community as a whole.
https://www.allwords.com/query.php?SearchType=3&Keyword=socialism&goquery=Find+it!&Language=ENG
Any of various political philosophies that support social and economic equality,
collective decision-making and public control of productive capital and natural resources, as advocated by socialists.
https://mnemonicdictionary.com/word/socialism
a political theory advocating state ownership of industry
http://www.thefreedictionary.com/socialism
Any of various theories or systems of social organization in which the means of producing and distributing goods is owned collectively or by a centralized government that often plans and controls the economy.
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The reason people like you define socialism as "the workers" owning the means of production, is so you can play the "not real socialism" card against all of the murderous, disastrous, examples of socialism that have taken place in the world.
Mondragon is a private corporation that competes for profits in a market economy. The owners of this corporation are capitalists: