It is "power over eSATA", or perhaps "eSATA with power". It's an eSATA port but with additional pins that supply power to the drive - which fixes an issue with eSATA that made USB 3.0 look a lot more attractive. Also known as eSATA-p and several other variations.
It hasn't seen wide adoption. It's been effectively replaced by USB 3.0.
Aside: I do have an older Dell laptop (E6520) that has an eSATA-P port. Dell made a "modular bay adapter" that would let you plug any of the devices that you'd normally put in the laptop's interchangeable drive bay (optical drive or additional hard drive) into this adapter, and then plug the adapter into the eSATA-P port. The laptop's docking station has an eSATA-P port also. AND the eSATA-P ports will accept USB 3.0 devices (that does not appear to be the case with the card you linked). All in all I really like this capability, but eSATA-P appears to be a dead end. Dell dropped the eSATA-P port from the Exx30 and later series.
As the product page you linked says,
This port can be connected as eSATA, PeSATA
Combine with our Power over ESATA cable ( not included in package ) , both 2.5" and 3.5 HDD can be supported without power supply from other sources.
BUT: That last claim ("without power supply...") is only true if your external drive is in an enclosure that also supports eSATAp. If the external drive just has an eSATA port it'll still need its own power source.
Since the mobile rack you want to buy is to be installed in your case, and is expected to be connected to internal SATA connectors, I don't think this card will do the job for you. It will only give you one more SATA port and you'd have to have a cable running from the card's external eSATA(p) port, somehow getting inside your case, and going to the back of the mobile rack.
See also https://en.wikipedia.org/wiki/ESATAp
(But... I may buy one of those cards, so I can use drives in those Dell adapters with my desktop!)