If you have a .1 header you could compare it to the connector and see if they match up.
What I’m looking for is the spacing between pins (although really I’d like to know what the actual connector is so we get the correct footprint).
edit: Actually assuming you want to make more of these, you will in fact have to figure out what the connector part number is so you know what connector to order to mate with the ones on the board. So look for a part number or a manufacturer’s logo on the connector is probably your best bet. I can’t see anything that says what the connector part number is anywhere.