Out of the several composers and thousands of compositions out there, let alone all those non organ pieces adapted to organ, who knows. I have a few recordings I haven't figured out yet. You could always ask the organist. That recording didn't strike me as fitting the style of any particular composer I know. It does sound older rather than newer, but is simple enough that there's no telling. When in doubt; Bach.

Well, I found it, but not in organ yet. 

It’s the prelude of Domenico Zipoli’s IV Suite. 

Was it worth all the effort?

I still haven’t “found” it because I wanted a good quality organ version of it, not piano or chord string,“professional” like the ones you find on YouTube of any other composer.

If anyone here can play the organ well, I’d consider paying for it.

It was played as the entrance procession at Mass.

Siri claims it’s Toccata & Fugue in F Major but someone told me it’s not, and indeed it’s not totally the same although some tones sound similar.

Can you ask the organist at your chapel to help you with it since he knows it already?  (He might be delighted that you enjoyed it so much.)

It didn't sound too difficult to play but I noticed that it has a lot of foot work with the pedals.

Finding the composition is the most important part. Which instrument it is played on is secondary. I was not impressed by that piece as played in your recording, though musical tastes are subjective, but it is important to be aware of the particulars of interpretation of the piece and the expression and articulation that goes with it, and organ registration, all of which can make a night and day difference in how it sounds. The question becomes, how do you want it to sound? I know I can be quite picky on this point. Sometimes I have two different preferred renditions of a piece. Sometimes I find I prefer not to listen to a piece unless someone were to combine the particular parts I like from 5 different renditions.

How did you find it anyway?

Yeah, sound quality is not the best (sounds better if you port it to iTunes though for some reason), there’s background noise, and I think I hear what sound like a few mistakes (touching the wrong key).

I’d like it to sound just like it does but with good quality and no apparent mistakes.

The way I found it is that months ago, the last time I heard it played, I asked someone who knows the organist (I don’t) and the organist said it was a prelude by Zipoli. I looked it up back then and since I didn’t find it in organ and didn’t recognize the other one, I thought the person was mistaken. This time around, having an actual recording of it (last time I didn’t) and with Siri guessing wrong, I looked up Zipoli again and listened to the preludes on YouTube played on harpsichord and you can tell it’s the same tune.

There’s another reason I want this music in good quality, beyond just listening to it, but that’s a secret.

You want just that 1:30 clip you recorded?

Music sheet attached.