The first and obvious failure of that logic is… well, maybe even without minimum wage anyone can make enough money to eat. While freezing in the dark, of course.
It’s not rocket science, and I’ll skip the political jabs, to calculate that a full-time job at minimum wage CANNOT make enough money for a single person to live an acceptable functional life. The cost of food, rent, and miscellaneous like clothes and transportation, even at a subsistence level, is well beyond minimum wage in most urban centers. It’s compensated for by living in substandard housing, going hungry and not having children.
Add to this a lot of the people who are in thi situation are there because of problems. There are a number with physical problems, and others with character shortcomings that make it difficult for them to hold a job for any decent length of time.
Most modern democracies claim to have respect for dignity and human rights. This usually translates into welfare payments, unemployment pay etc. - so the poor do not have to starve under bridges or beg in the streets mainly to survive. Similarly, people tossed out of work because of the economy, should not after two decades of work suddenly have to sell all they have just to survive the next year or two.
As Gus G points out, the interview is about stupid people showcased to display their stupidity. The interviewee obviously seems to be of the belief - “I made it with a bit of work, obviously they can.” This ignores the issues of self-esteem, intelligence, education, and ability to stick to a task (ADHD), let alone basic mental health problems. In my experience, many of the minimum wage employees are either unqualified to do better, incapable of doing better, or in other circumstances that prevent success. Telling them “it’s all your fault if you don’t do better” (a) isn’t true and (b) not the best of motivation.
There’s nothing intrinsic about a democracy or a capitalist society that guarantees nobody starves. However, there are not really any purely captialist societies. The welfare state elements of most modern societies are what currently guarantee people are fed.