No you don't need a mixer to hook up monitors. You can hook up monitors to any professional audio device on the market. A mixer is good for multiple signals, straight hardware setups, the routing of signals and adjusting of levels, eq, etc. But most of the effects you get from a basic under $500 mixer, are what you pay for. You can get way better effects from VST's. If you have a large rig, a solid mixer is essential. However, for just a few microphones, monitors, a pair of headphones, or whatever, you don't need a mixer. Honestly, I would never buy a piece of hardware just because of the software that comes with it, all of the software is entry level / restricted versions anyways. For instance, you will be using Cubase LE, which is rather limited.
As long as you do your research you will be fine. Your choice will work, I am not sure if that specific Alexis product works as a sound device driver-wise on your operating system, for instance does it even have a power switch?