Let's clear up a few things first.
You can record a digital piano in two ways:
Audio recording. This records the actual sound that the keyboard makes. To do this, you'll need to route one or two of the audio outputs of the keyboard to some sort of audio interface.
MIDI recording. This records the notes that you play in a digital format. It does not record any audio information. You can play it back using the same keyboard, and it will sound the same. But you could use a different playback device, and it will sound quite different.
So, to address your question, I think you want to use audio recording, but you are currently just recording MIDI. The good news is that audio recording is usually pretty simple to play around with.
First, you don't need MIDI cables (the round plugs with four prongs, technically called DIN connectors. You need some audio cables. Usually that will be a 1/4 inch jack, mono or stereo.
Then, you need an audio interface. You can buy a specialised one, but I'd recommend playing around with the microphone input on your computer. It might be a bit noisy, but you should try it out first. It'll help you get an idea of how this all works. You'll need a 1/4 inch to 1/8 adaptor or two.
Once it's plugged in, you'll need to record it. I'd recommend playing around with Audacity to start out with. It's free, simple, and will give you an idea of how this all works.
Once you've got a taste, you can spend some more cash to get some better equipment. But I'd recommend trying all this out on a cheap/free basis first.
As a variation, you could try and record the keyboard using the camera itself. Often a camera will have a microphone input. You could try using that.
If you want to record other audio simultaneously (you speaking, or something like that), this might not work. The microphone input will often disable the internal microphone.