If an algorithm is on another server, you have to pump the data over there, process it, and pump the results back. If the data size is large, transferring the data will take some time. Thus, the algorithm must require substantially more time than the data transfer. Render farms are the classic example.

There are some commercial desktop applications which do this. Autodesk Fusion is one. Some of the more compute-intensive tasks are sent to servers at Autodesk. If you don't like that, you can buy Autodesk Inventor, which is more expensive and requires a big desktop machine locally. (I've used a 24 CPU machine with Inventor. If you're doing finite element analysis or injection molding simulation or ray tracing rendering, it can be worth it.) Autodesk 123 Catch (3D model from photos) also works that way, which allows running it from a phone app.

Another possibility is that the algorithm is proprietary. This comes up with oil well data analysis. But the data is proprietary too, so everybody has to sign tough agreements.

This article mostly looks like a way to have micropaments (maybe not so micro) for software accessed from servers. If you're running on Linux, it's hard to license software to a server, what with virtual machines, cloud systems, and containers being started and stopped.