I came across this model and I was wondering, how would something like this get machined?
That part is likely two different parts, one of them pressed inside the other.
Each part could be made in many different ways. How they were produced highly depends on what material they were made from.
High part number productions will often start with a ‚near net shape’ mold, and will be cast to almost what the final part is in dimension this saves fabrication time and material costs. Even highly complicated engine parts or entire blocks will be cast if they can be.
After this the parts will go into machining, if this is again, a high production part, they will likely be highly likely fully automated cnc machines. 4 Axis would be enough for that part with only a single part change for final contour. Depending on the part and tolerances, they may be pressed together first then machined or any combination.
After this they may go into whatever post processing that needs to be done, like pressing, hardening, plating, cleaning etc.
They have lathes with special tools which can hold the odd parts firmly to be worked on. Watch around minute 1:25.
I think I've got what you are asking.
The most probably response is. At the end of the radial holes (the big ones) there's another radial hole matching with the diameter of the axial holes (the litle ones).
And this could be machined either with universal milling machine with a divider or with a cnc machining center (most probably).
Without understanding the whole sistem I can't be sure but the probability like this higher because the sistem should work like on car's piston sistem where the gas and oxigen enter and there's one way valves both in inlet and outlet.
Looking at the image looks like all holes should be for only one function (inlet or outlet). And on the other side there should be the other function holes (probably in the exact same alignment.