Knowing nothing else, it's hard to know if this is good or not. It's 16 requests per second. Are those requests something like "Render a support article" or are they "Give the user a ranked feed of what they should see on their home screen"? Is most of the logic run by the web server or some combination of app servers / backend services behind it? What kind of hardware does the web server have?
All of those would affect the answer, and would preclude being able to guarantee "up this by couple orders of magnitude"
Well, to give you an idea, I am working on an service that implements rather complex business process involving fetching data from multiple sources, parsing binary blobs with market data in proprietary format, saving results to a database and so on. And it does around 10k requests per second on a single relatively normal node (8 cores, 64GB ram, etc.)
And no, it does not require any special tricks. It is regular Java / WebFlux / REST / MongoDB backend service.
CPUs can do really a lot and if your node processes 16 requests per second on a multi-core machine then you are using billions of clock cycles and gigabytes of possible transfer to memory for a single request. Something is not quite right...
As a somewhat imprecise example, if a single "request" requires sorting 2.4 billion integers, then a 2.4 GHz CPU with 16 cores will be able to process at most 16 RPS no matter how much you switch from JavaScript to Java or if you write assembly.
At the end of the day efficiency is ultimately a business problem and not a technical problem and is rarely the thing that tips a project (Clubhouse in the article) from being profitable to being unprofitable. It's usually an investing question - I have X engineer-months to spend. I can cut costs by Y by optimizing stuff or get Z more profit by building a feature. I will choose to optimize stuff if and only if Y>Z as it returns more.
Clubhouse's major costs are probably bandwidth and engineer time rather than servers. That is to say, even if efficiency was infinity for compute (i.e. server costs magically went to zero) it would probably not change Clubhouse's business proposition that much.
More to the point, I think you are uncharitable at best when you say elsewhere that other frameworks and languages won't require more development work. These frameworks (and the choice of language being implicit in that) are specifically designed to reduce development work. Let's examine for example garbage collection. Garbage collection is undeniably more wasteful than other solutions to memory management, absolutely. But would you really argue that garbage collection does nothing to reduce development time? I find that extremely hard to believe, empirically and subjectively having written programs in many environments including bare metal, reference counted or otherwise semi-managed and garbage collected languages. And so it goes with all of the choices these frameworks like Django and Rails take. And it's getting better with time as things like JRuby are developed, inefficiencies in Rails or Django are removed, etc.
All of those would affect the answer, and would preclude being able to guarantee "up this by couple orders of magnitude"