I agree that it isn’t very similar to modern Capitalism at all, but the means of production would still not be state-owned or managed, so the only socialism going on would take the form of unions and government welfare, which is more similar to early 20th century american capitalism than it is to most socialist movements of the past 100 years.
The definitions of socialism and capitalism are constantly in flux though so assigning a simple name to a nuanced economic framework will always be reductive and confusing.