OK this one goes out to the OP ,
I think you have gotten some excellent feedback and advice from a number of people in the know .
In a nutshell there is simply way too many artifacts present in the recording you want to transcribe / make a Midi file of for an easy audio to midi conversion to happen ...
May I suggest something to you ?
For this recording I happen to think that we are all going about this the wrong way

just because the door is closed doesn't mean we cant open up the window .
Please allow me to explain to you why I feel this way ...
I saw the video one time ...visually it was impressive , but I don't care about that ..
all the time I have spent with the tune you put up has been spent in SONAR and Transcribe ..
The young energetic piano player has my respect for his performance , he did a wonderful job during his performance , yet he is not playing a thing that has me quaking in my boots over here ....
Before I say another word about music , let me explain to you a way of thinking that unlocks the limitations many of us willingly place upon our self's ....
Often times when another human being or a musician plays something we want to learn it means we have entered into the gravitational pull of the law of attraction ...they are embodying something we would like to express.
The interesting thing is the very reason we can recognize that in another person means that we already have it ...
If we did not have it inside our selfs we would not be able to recognize it in another ....
One of the frailty's of the human condition is "to not own it " by saying well he can do that but I never will be able to do that ...
OP I know that you don't feel that way because you are doing your best to make a midi file of this tune
for your son ....yet it has to be said ....and I'm gonna say it ....
What that guy played , I can play also ....
OK , I put your file in Transcribe and I was able to play along with it on my guitar and nail at least half to 2 thirds of what was played on the piano ...since I play guitar I concentrated on 3 distinct elements of the song ...one at a time
The Bass , The guide Tones / Chords and the melody / fills ...
I did this at 70% speed and after spending some time with the song I'm not over here quaking in my boots ...
If You take away the visual , then concentrate on the 3 elements I have mentioned , +roll up your sleves and do a little work you will be able to transcribe this song ...
Having gotten that far after an hour or so I wanted to go deeper ...
I took the song and beat mapped it in SONY Acid Pro 7 only because it was fast and easy to do ....
I didn't do a perfect job but the song clocked in at around a use able 150 .9 BMP ..it doesn't have to be perfect .
What I did next was set the tempo in Acid pro to 120 ...the reason for that is I wanted to export a modestly slower file into SONAR Splat at the default setting of 120. BMP ...
When I imported the file into SONAR I made sure to import it as a split mono ...
The reason for that is because once imported into SONAR it was easy to see that one side of the file is bass heavy and the other side isnt ...this plays into it ....one side has less artifacts that are distracting ....
If you happen to still be w me I'm suggesting that you may want to try some of what I have been suggesting unless you think I'm plain old nuts
When I was in SONAR i took my guitar and I played the bass part along with the song ...then I recorded some it it along with one side of the track ....BTW it is important to be able to switch sides of the file to hear all the nuances ...
What I did next was to put an instance of true pianos up as a synth ...then I slid my guitar track over to the midi and had a decent section of the bass track .....VIA the ARA conversion ....
then I took a little bit of the song and played some of the guide tones , recorded that and slid it over to another Piano since I can only get one instance of true pianos happening ....
Now here's the kicker ..I haven't done the whole song I'm not Einstein but I have done enough of the song to be able to tell you that getting this one down is very possible ..
Now here is a little trick you may want to try ...If you have done some of what I have suggested you will have played along with some of the song , laid down some skeleton parts of some of the songs arrangement ...
if you have done that by that point you will have sections of the song where you can mute the original file ...
even if it is for only 20seconds ....
Now is the time to pull out the big guns
Do an audio to midi conversion with one of the sides of the imported file , which ever one works the best ...
What you are gonna get is a pile of POOH ,,lol but I know a way out

Double click that monstrosity of a midi file that looks like fly $hit and open it up in SONARS piano roll ...
now is the time to make a hard ball decision ...do you want to play with one side of the audio file or do you want to play with some of the parts you tracked ?
Here's what you are gonna do , you can listen if you want , hit play while you are in the piano roll ...listen
the midi conversion is all over the place right ? good ....
While you are listening /looping delete all the bass notes from the low end in the piano roll up unto the point of a Bb below middle C .

What you will find is most of you problems have just went away ...that's where all the garbage was from a poor audio to midi conversion ...by that point you should have some chords that are not exactly right and the guide tones and the melody ...
Bear in mind there will be more editing to be done but you are gonna be a lot closer in the ball park ...
I'm running out of steam over here my friend , if you don't dig what I'm saying here ...that s OK
Do me a favor and at least consider approaching this song as three distinct elements .
A bass part , A chord part and a melody / fills ..if you do that you will be good
all the best ,
Kenny