According to this datasheet that I found in a google search, they're calling that a "spring pinned socket."
Unfortunately, I wasn't readily able to find anything similar by searching Google, Digi-Key, and Mouser (where I found the datasheet) for that term.
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Upon re-examination of your photo, there's technically no 'socket' on your PCB, just looks like they drilled a large # of vias/thru-holes & soldered in the pins individually.
Based on that observation, I did a little more digging & think you might be able to find a suitavle replacement somewhere in these results.