No of course, you don't have to, if you don't want to. I'm sure you will enjoy the music by simply playing it. The power of great music is sometimes irresistible.
But let's start with understanding how usually people sight-read music. They play notes that are written in the score. In other words, they read music. But reading music is not the same as understanding music.
You can play the notes, but often it's quite tricky to understand what exactly these notes mean. So one of the best ways to start practicing and understanding your favorite organ piece is to be able to analyze it - its structure, chords, tonal plan, cadences and modulations.
Since cadences and modulations are rather advanced concepts in music theory, we start with simple three-note, and four-note chords and their inversions as well as five-note chords without inversions because they are used not as often.
So when you learn the chords and you try to recognize them in your organ compositions, then suddenly entirely new tonal universe opens up. It's like a hidden meaning of these notes will become apparent to you.
It's similar what composers do - they don't just writes notes at random - they have this tonal plan which fits their idea of the piece. And inside this plan obviously are many different chords and their inversions.
So for example, if you know a D65 chord and you try to find it in your organ piece, imagine how different will your playing of that passage be. You not only will be reading separate notes (like B-D-F-G) but you will suddenly realize that it is the chord, not only the combination of notes that don't mean anything.
Sure, they might sound beautifully but you might not know why. But if you knew that it's a D65 chord (the 1st inversion of the D7 chord) then what happens is that your eyes and ears will open up to its meaning. You will also start looking for other appearances of the same chord in other keys.
Here I'm talking about only one chord but imagine if you knew several other chords, then your analytic skills will be so much more powerful. You will take the score of the piece and just by looking at it you will know the meaning and function of these chords.
And it's very helpful for your sight-reading because you will not be playing random unconnected notes, but rather chords, their combinations, arpeggios, and various other patterns.
Chord mastery also helps you to memorize music because again these chords and notes will speak to you and you will not memorize automatically (using muscular memory without thinking about its meaning).
So I really strongly recommend you start learning some of these chords and you will begin to see how much more meaningful the organ music will become for you.
And the most powerful benefit of all (at least to me personally) is that your musical curiosity and creativity will be enhanced as well. You will be feeling like an explorer who finds a new and uncharted territory.
Lately more than one of my students and readers have written me about the joy of musical discovery which obviously leads to the desire to create something of their own (either on paper or as improvisation).
If suddenly you will start to feel the urge for creativity, know that this is a good thing which might lead you to some really exciting musical discoveries and adventures, if you choose to give them a try.