Those spacers are acting as alignment pegs, or guide pins. I've not seen those specific ones before, and I'd hazard a guess that they've been custom machined.
I have personally used the GP series of pogo-like pins (GP = guide pin) such as the GP-1 or GP-1S.
https://www.ebay.com/itm/2-Pcs-GP-1S-Pogo-Guide-Spring-Pins-for-Test-Station-Dia-3-2mm-200g/371632228964I've also just used standoffs with male threads lined up with the PCB mounting holes, or a simple plastic frame cut to the outside shape of the PCB.
For pushing the board down onto the pogo pins, you would typically use some kind of clamping mechanism as part of the test fixture. Often this uses a sheet of material with multiple push rods attached, so as to press on the PCB between components and spread the pressure evenly. You will often see white ones like these in use:
https://www.aliexpress.com/item/Free-Shipping-100Pcs-6x40mm-Point-Ended-PCB-Test-Fixture-Parts-Plate-POM-Pressure-Bar-White/32712287035.htmlDo a google image search on "pcb test fixture" if you're not clear on what I mean. There are lots of methods depending on the shape/size of PCB and the mounted components.
In this case it looks like the weight of the PCB alone might be enough for the pogo pins, at least in that photo (possibly not ideal to trust that for production testing).
It is worth noting that you can buy pogo pins with different force ratings, which can be useful if building a jig requiring a huge number of test points, or for testing a delicate circuit.
Sometime you also want certain pins to make contact first, or have a higher current rating - so you may make use of several pogo pin styles or mounting methods.