In simple words...Yes, lenght matters
.
Outputs are joined to get (roughly) 50 Ohm output impedance and match the cables impedance.
You will get delays and your signal will be not that clean as when you bodge the resistors with matched lead lenght.
So actually your etched ciruit may perform worse than this solution.
Have you ever seen tracks on a pcb snaking around? That's to match the lenght of the tracks because of delays. Of course you could do so too.
Very nice design btw you did. So try to match the lenghts and it will be perfect.
(It will work anyway ok).
Try to play with the cap and resistor value for the oscillator. The frequency is like 3 to 6kHz (when i remember correct) and doesn't matter too much, but you want the fastest edges possible.
(I have build this thing too, long ago...the bodged version
).
Search the other video of Alan. I remember he has compared this (his) circuit to another one which was made clean and nice but didn't perform as well as his.
In the series of 74 hex inverters there are slower and faster chips availiable. Pick a fast series like the 74hc14 or a faster and rise time should be in the area of 3-7 ns. I see, you did in the schematic, thats good.
There are even
much faster edge generators which work with an avalanche voltage on a transistor. Pulses with sub-nanosecond rise and fall times.
(Like
http://www.aholme.co.uk/Avalanche/Avalanche.htm for example...just google" Avalanche Pulse Generator".)
Just watch Alans videos and you will find an example for this too (btw i highly recommend his channel).
Have fun, Tom