The HP HDD caddy has a 90 degree IDE pin converter. You need to carefully pull that off, then remove the drive from the caddy (4 corner screws.) It can then be read by any 2.5 IDE connection.
You picture shows that has all been done. It looks like a standard 2.5-in IDE drive connector. It provides both power and data.
This picture shows the drive still in the caddy, but with the 90 degree adapter pulled off: