It is possible to use Kitcore without having a MIDI interface. Kitcore includes MIDI beats which can be brought into your DAW and used to trigger the drum sounds.

Now if you are looking at the Kitpads, those could be triggered via a mouse, but ideally you would want to "play" them. For that, you would want some sort of MIDI device and a MIDI interface. The MIDI interface you found should be sufficient. I have one and used to use it until I got something different. For the MIDI Device, something like the Korg PadKontrol or Akai MPD24 would work. They make it easy to play MIDI notes. Of course you could get a small MIDI keyboard instead.

It comes down to...do you want to use the included MIDI beats or write your own. If you want to write your own, you would be best served by having a MIDI device and interface...simply because mouse clicking doesn't give you that FEEL.