There's something called "economics", much like there is something called "psychiatry". [Maybe we need more sociology in policy-making. Maybe economics is too narrow a view on the world. But it is a specific field of study.]
There are good reasons to be critical of psychiatry, but it's a red flag if someone tries to pass palmistry off as psychiatry.
The problem here is that economics does have some prestige still, which is why predatory political activists try to pass their "heterodox" writings as belonging to it.
Economics is a science. You get an idea what's 'pseudo' or not by working in or familiarizing yourself with the field. Say, The New neoclassical synthesis is very much as standard as it gets, whereas Marxist or Austrian economics exist on the fringes.
In general something is pseudo-scientific if it operates outside of the formalisms or tools of that particular discipline, especially if it pretends that it does not.
"Modern mainstream economics is sure very rigorous — but if it’s rigorously wrong, who cares?
Instead of making formal logical argumentation based on deductive-axiomatic models the message, we are better served by economists who more than anything else try to contribute to solving real problems. "
I'm not sure what that critique has to do with the original question about the distinction between science and pseudo-science, but I'll respond anyway.
The purpose of science is the generation of knowledge, it's to have a formal understanding of a system and essentially a language and methodologies to make inquiries.
Economics as a science does solve real world problems, but it's not the dominant purpose of a science as such. It's the task of problem solvers to take scientific results and then turn those say, into actionable policies. Scientific work does not exist for the purpose of solving 'real problems' in the sense of being subjected to that goal. Scientists are not engineers. When Computer Scientists talk about Big-O complexity they often do so in a way that's not really applicable to real-world software development, but that isn't their job.
That said economic theory actually does very much factor sucessfully into decision making. Be that macro-economic policy, central banking, the design of markets and incentives, and so on.
Economics is not something that can be tested easily on a large scale, so most of it becomes about trying to explain why things happened in retrospect.
