Ok, it took me a while to figure this out, but I think I've got it.
The short answers are
jasonmads wrote: ↑Fri May 28, 2021 5:06 pm
But now I'm not sure why it is "working" with the GATE-TRG, the trigger should arrive at the BOOL before the Threshold signal.
The "acoustical" result (kick and snare changing randomly) is what you would expect to hear, but actually kick and snare are switched.
jasonmads wrote: ↑Fri May 28, 2021 5:06 pm
Is a trigger a single sample in length?
Yes.
The long answers
jasonmads wrote: ↑Fri May 28, 2021 5:06 pm
But now I'm not sure why it is "working" with the GATE-TRG, the trigger should arrive at the BOOL before the Threshold signal.
I don't own Andrew's GATE-TRG module, so I will use my own gate-trigger-converter. It won't make much of a difference, I suppose. I have recorded signals at different points in the patch to check what's going on timing-wise. This is the patch I've made:

- patch.png (934.9 KiB) Viewed 4210 times
The upper cabinet is basically your patch, except for the gate-trigger-converter. The lower cabinet uses the
Sample Delay module to compensate for the delay.
In this image you see the recorded audio files from the first, second and last
VM Recorder in the lower cabinet showing the difference between the direct trigger signal and the delayed trigger signal. The output of the Sample and Hold module was greater than 0, so the Over Out on the Threshold module goes high.
The past samples between the direct trigger and the Sample Delay output is marked. I was not able to confirm this, yet, but it seems that every module introduces a 1 sample delay anyways, plus 1 sample delay from the Sample Delay makes the 2 samples that are marked in the image.
As you can see in the audio file in the middle, the trigger signal does not coincide with the gate signal (Direct trigger + Over Out). When the trigger signal gets delayed it coincides with the gate signal (Sample Delay trigger + Over Out). Consequently the Boolean Logic module won't output anything, because trigger and gate are not high at the same time (Bool output @ direct trigger + Over Out). This only happens when the trigger is delayed (Bool output @ Sample Delay trigger + Over Out).

- Over Out - low 2 high.png (110.72 KiB) Viewed 4210 times