@immatthewj As Eric Squires alluded to, the value of a 3-Wire plug into the wall will offer the connection to earth ground necessary to provide a shield for the cable. Whatever cable you buy, every manufacturer I’ve seen on record recommends a shielded cable. You can’t have a shield without a connection to an earth ground. The purpose of the shield is to provide a path by which to ‘drain’ EMI (electromagnetic interference) present in the environment from other electromagnetic producing components like transformers, speakers, other power cords which aren’t shielded. In your case it may be an advantage that there is no third pin on equipment, as it prevents the condition in which the shield is connected at both ends, which some interconnect cable incorrectly do. If the shield is connected to ground at both ends, it is no longer a shield, but a conductor. (Although, in deference to Ralph of Atmasphere, it all depends on the implementation of internal circuitry.)
So, the two pins on the equipment end means that they have isolated the equipment from earth ground. My understanding is that this is an older, and some say better, way of making equipment safe. These days everyone has jumped on the GFCI (Ground Fault Circuit Interrupt) bandwagon, which requires an earth ground connection as an alternate path back to the utility. Regardless of the method, the purpose of fault protection is to carry the current back to the utility, without going through your body.
l hope your new power cable enhances your experience of the music in your system.