The Xonar Essence STX will only put out two channels of sound. Mind you, those two channels are the most exquisite. But that's what the card is for... people who have high end audiophile headphones who want to enjoy a pristine music listening experience since it's more easily achieved in a set of headphones as opposed to a set of speakers.
The Klipsch ProMedia 2.1 speakers are a fine set of speakers, but I'm not sure how much they will benefit from the Xonar. It certainly wouldn't be any worse. You're not going to get any surround sound out of them unless you have a receiver that can decode Dolby from the two channel audio. Or if you use the digital out on the STX to a receiver, but then you're not really using the sound card for what it's made for.
To summarize, get the Xonar Essence STX if you are going to mostly listen to music with high end headphones that are made for accurate, distortion free music reproduction (like professional monitoring headphones).
If you want more options, like the ability to (in the future) hook up a 5.1 or 7.1 surround speaker system for gaming or Blu-ray movies, then you may want to utilize another sound card or even just the stock motherboard sound card if it has hookups for multichannel audio.
The STX is awesome at what it does because of it's high end components and attention to minimizing electromagnetic interference, but that may or may not be what you want.
If you still can't decide... don't get the STX. Try your speakers, headphones, etc... with the onboard audio and see if you like it or not. If it sounds awesome to you, then great, go no further. However, if you're not satisfied with the quality of your sound, and you have the money to burn, then go ahead and get an STX.