Well the video portion looks like it was done with a cell phone. It's not very sharp and the color balance is way off.
The audio is better but of course it can be better. The piano sounds much better than the strings, But with synthesized sound it is always hard to know if the problem is in the recording or the source.
The typical way you make these recordings is NOT to use a microphone. Patch the output of the piano to the recording device and it's a straight electronic connection, no microphone.
An even higher quality way is to record the MIDI stream and then later in the DAW you can use higher quality virtual instruments than what you have in the piano. Especcially those strings. You have time to audition several and can tweak the sound until it's perfect. This is a totally digital recording method with no analog path. The sound is as good as your virtual instrument.
Here are a few piano recordings. Theye are "virtual instruments" made with no microphones or real pianos. You could do this via MIDI. This is pretty good for the money, not really expensive. Liten and see what you think.
https://www.pianoteq.com/listen_by_instrument
Here is a youtube demo of what you can do with the Apple's string synths that a "free" inside Logic. This sound is much nicer than what is in most digital pianos. It is included with Apple's Logic.
http://youtu.be/eq09iBPfgKE?t=5m50s
Here is a sample of string composition played entirely on a keyboard. The guitar is played on the same keyboard. Just to show that there is room to improve over Apple's product.. (would be sad otherwise wouldn't it?)
http://media.soundsonline.com/mp3/2459_Sampled-Not-Stirred.mp3
Another one played on keys. The vocalist is also not real she is synthesized and played with (guessing) the right hand. You can hear it it is only voiced vowels and it's slightly repetitive but sounds real. The strings in this might be what you were looking for. Again no microphones were used it's MIDI from the keyboard to the computer
http://media.soundsonline.com/mp3/2581_Ulthuan-Live-Performance-Gold.mp3
So in short, your video is good enough to communicate the idea but could be much better without spending a lot of money. The limitation, I think with your setup is the quality of the built-in strings, then after that the recording setup looses why I call "brightness" but is not bad for a cell phone.
Technical summary: Recording from the line outputs allows you to bypass the speaker and microphone so their quality or lack of) becomes not relevant. Next using MIDI allows you to use much better sounding instruments that run on your computer, not inside the piano. (MIDI only sending the key press data, not audio.)