The preview window is not representative of how that software works. The renderer is slow.
Once you start the encoding, all the work is done in the background by x264 and the audio encoder.
Don't know what to say, maybe you didn't install MeGUI properly? Did you install AviSynth as it said during installation, did you accept to install those presets during autoupdate? etc etc...
The whole installation is not that user-friendly, I'll admit.
Also, it's not really relevant that the image is distorted in the preview window. You should be able to give the application a "hint' as to what aspect ratio is the correct one in that preview window, but basically the encoder will encode 1440x1080 and the proper aspect ratio is generally saved in the container used (mp4 or mkv), not in the video stream, so it can be corrected later on even if it's incorrectly set by MeGUI.
later edit: and don't put down the application if it's slow on the first tests, you really have to go and check the x264 settings/profile and tweak it to get to where you were in handbrake.