i don't know anything about genesis car's i assume made by hyundai? but i can tell you about GM and the 1998-2002 camaro/firebirds having a similar type clutch slave cylinder.
think logically a second about GM and how it might be done on the assembly line, and the thought or lack of thought that was put into things. a car rolls off the line every 10 minutes or something, fast enough you know 2 or more technicians aren't bleeding the clutch system on the assembly line. there is a quick disconnect fitting on the gm slave and also on the end of the line coming from the clutch master cylinder, both units are sealed when disconnected so now brake fluid escapes. the gm slave comes already filled with brake fluid and bench bled from the supplier, and is then bolted onto the transmission prior to assembly of the trans to the motor. if u ever watch how it's made, it's very common for automakers to roll the drive train separately down the line then marriage it with the body... with the body having the clutch master cylinder and line hanging down which is also pre-bled. so once those two halves of car come together, 1 guy simply plugs the clutch line hanging into the slave cylinder fitting barely protruding from the trans. the design was crafted for manufacturing assembly and never for the mechanic at a dealership working on the car. to properly service the slave you need to drop the trans and remove the slave and bench bleed it. like you noticed (which nobody else ever does) is how the bleeder on the slave is orientated and if you have the car level on a lift with slave/trans installed on car there will always be an air pocket in the highest point in the slave because the bleeder valve is not the highest point on the slave when installed in the car. now if you can orientate the car so that the bleeder valve is the highest point then you might have a chance, however don't forget about air anywhere in the line up to the clutch master cylinder. 1 pump of the clutch pedal pushes very little fluid, any air in the line is going to move a few inches then bubble back upwards... which is why "gravity bleeding" is ridiculous.
and you can read countless threads on forums about people bleeding their clutches and still having problems, this is why.
when you bench bleed a slave, you fill it with brake fluid and ensure there is no air in there, then compress the slave and quirt out excess brake fluid. then install it on the trans, the slave will be completely sealed and more importantly fully compressed so when u install the trans the slave doesn't hit the clutch and prevent mating the trans to the engine/bellhousing. with no air in anything, you connect your clutch hydraulic line and the slave expands under because of it's spring and sucks down clutch fluid from the master, then all you do is top off the clutch master resevoir.
and why is there what looks like a half clam shell in your pic?