The left hand and right hand line up just fine - the left hand starts off with a constant pulse, and the right hand plays two notes for each left-hand note - so the title is a bit misleading, but I'm not sure what to suggest instead, since I'm not entirely sure what the real problem is.
Are you asking how to learn to play the song using that video, or are you trying to learn using the sheet music and you've linked the video so we can hear what it sounds like? Because the sheet music will contain a lot of crucial metrical information (time signatures, bar lines, beaming patterns) that a piano-roll-style video like that is missing. Especially for a piece like this, where the time signature is changing fairly often.
Most of the guidance I know for learning pieces involves breaking it down using that structure - practice a bar at a time, or two bars at a time, or one beat at a time, things like that - which is harder to do when none of that information is there to see.
In terms of your question about "bringing the hands together without a reference", though, I can offer some thoughts. Most importantly, you should never be "without a reference", because the music has an underlying pulse and both hands should play relative to that. If you don't have a sense for the underlying beat of the music yet, then use a metronome app (or similar) to generate that pulse, and count along to it as you play each hand: 1-and-2-and-, and so on (either counting out loud, or in your head, whatever works better for you).
Figure out where the bars are so you know when to reset your count to "one" again; if you're not sure how to identify the bars then that would be worth asking as a separate question if it hasn't already been asked. (There isn't necessarily a single unique "right" answer for how the music is divided into bars, but there are definitely wrong ones.)
Practice each hand separately while you're counting the bars, and learn how to play each hand relative to the underlying beat that you're counting. Make sure you line the hands up correctly with the beat; it will be harder to 'undo' the practice if you do it wrong. At least for the opening section, the left hand arpeggio always begins on the beat; the right hand sometimes doesn't.
In case this is the source of the difficulty, I'll try and say that again a bit differently: you are trying to count along with the underlying beat of the piece, not to count along with the notes you play, even if a lot of the time the notes do happen on the beat. The first left hand note will come on a count of "one", because the first left hand note is on the beat; the first right hand note will not come on a count of "one", because the first right hand note is not on the beat.
(If you practice the right-hand alone counting the first note as "one", then you will struggle to put the hands together, but the issue isn't really with the hands-together part - the issue is that you aren't playing the right hand correctly.)
Once you can play both hands relative to the underlying beat, then you can put the hands together slowly (while still counting along) and they should line up correctly.