Pin size is diameter of the pins, 0.78mm. 0.78mm would be very short if it was the length!
Like Carpet says, that looks like it might be a TFZ/NX7 connector. You can use a regular 2 pin with them but you're better off using the proper connector which has a plastic shroud that goes over that protrusion, it makes it much more secure. Cable looks like this, it's the fourth most common connector after 2 pin, MMCX and QDC/KZ C Pin. QDC/KZ C Pin is another hood/shroud type of 2 pin, but with a rounded edge hood rather than squared, and that goes up more. They are not compatible.
Pretty easy to find, some cables will only do those three but many will do TFZ/NX7. I recommend Xinhs, I have this connector type from him on a TFZ No 3.
What IEM are you using?
This is recessed 2 pin vs normal 2 pin, you have recessed 2 pin. But it looks like you need a shroud/hood type of 2 pin.