I see no reason why that card wouldn't work, your computers PSU should be sufficient and your new card uses the same PCIE3.0 slot as your old one. The picture you posted isn't loading for me, possibly because the internet is really bad in the campus library where I am now. Assuming your current card is not water cooled, you should just have to unscrew a screw fixing the port end of the card to the case on the inside. Then there will most likely be a little lever at the other end that releases the card from the PCIE3.0 slot.
Drivers should not be an issue I will eat my hat if they don't have working drivers for Windows 8 64 bit. Once you physically install the card, connect your monitor to it and boot up your computer. Chances are the resolution will be really low (so everything will look ugly and huge) but don't panic it everything will look beautiful again once you install the new drivers. You should still install the new drivers even if everything looks fine. Go to AMD's website and get the Radeon R9 280X.
Hopefully this helps!