In the background, I see the DAW is playing tracks - so this may not be arpeggios coming from MOXF at all - but rather sequenced content on the DAW.

As a side note, it's fairly difficult to search for arpeggios if you need to "match" something in your head unless the category + name gets you close enough. If I'm looking for something with a specific distinctive rhythmic pattern - there's not a way to search that way. Nor is there documentation with this information provided. If I want something that's a fairly basic rhythmic pattern for a guitar strum - there's not a way to do a search for that. And this kind of feature would be helpful for bass lines or other ARP patterns.

Very needle-in-the-haystackish. It'd be a fun coding project to solve (for Yamaha or 3rd party) in order to enhance harnessing the potential of all those presets we have inside the keyboard.

I believe if you have a groove or guitar riff or bass line in your head, Record it.
Use the Arpeggios for when you are looking for inspiration (looking for input from the “player”).

Of course, there is way to intelligently search for it! If you hired a guitar player for your band and asked them for “a fairly basic rhythmic pattern” guitar strum... you’re basically asking the, to write the part.

Your description would need to define more than a fairly basic rhythmic pattern - that pretty much says nothing to the player, but “don’t go all unique on me”, keep it simple... so if you find yourself frustrated when going through trying different Arp phrases, perhaps you’ll never find it.

But if you take the approach — where you are looking for something that sparks an idea, because you are looking at them differently, you’ll likely find something without the frustration. It’s when you are looking for something specific that you get frustrated. Because each one that is not close interferes with what you have in your head.

Since almost any MIDI data can be converted to be an Arp Phrase (within the limits of the User Arp rules), if you find something close, it might be worth attempting to manipulate/edit the data with an appropriate tool.

Extra Credit:
In the MODX, you can create backing Parts that playback from selected Parts, while you use other selected Parts to play on top. When demonstrating the MODX, I often use Parts 9-16 to playback from a .mid File, while I play my lead sound from Parts I Setup in slots 1-8.

This way I can demonstrate several lead sounds, in context of single song... switching seamlessly between my lead sound, as necessary. Controlling effects and volume of all Parts using the Super Knob and Scene recalls.

So... I have no way of finding out what that arpeggio is...

It sounds like some sort of organ...

There's always room for improvement. If I'm collaborating with a bass player - I would rarely give no context for the inspiration I'm trying to get from him/her. I'd present some boundaries such as the style and some motifs such as drum beat, guitar pattern, etc. so they have some information as input before they output their twist. This is a two-way dialogue which is closer to what I was suggesting than the primarily one-way inspiration of sifting through arps without the ability to give more dimensions of input to the search engine.

As the catalog of content grows - ways to help manage this content will help differentiate and also help address concerns that come up about the needle-in-a-haystack feedback.

I still don't think what you're looking for from the video is an ARP. Maybe Katsunori UJIIE has notes what he did on that video. https://www.sitekatsunoriujiie.com/