Yeah, that schematic seems to match the stripboard layout you posted. And I agree with the criticisms on that stompbox forum.
The biggest problem I see with it is the huge DC swings at the output when you use the stutter effect. If you use it with an amplifier with decent bass response, you may be able to see your speaker cone slamming against its suspension limits in time with the stuttering!
I also agree with the comment about avoiding the LM386 in guitar pedals. I've successfully avoided the LM386 completely, and have been glad that I did! It will introduce its own distortion, which may be considered desirable by some people, but that method of producing the stutter (which is just a tremolo with a square wave for amplitude modulation instead of a sinewave) is not a good one.
BTW there's a similar design, also on instructables.com, which you should also avoid, presented as a tremolo (which it isn't). Avoid http://www.instructables.com/id/Make-Your-Own-Tremolo-Effects-Pedal/
There's a collection of schematics of existing effects pedals at http://www.diystompboxes.com/pedals/schematics.html
If you want to get into experimenting with amplitude effects for your guitar, I recommend the LM13700 IC. It's effectively a dual amplitude modulator - each half takes a signal and either amplifies or attenuates it according to a control voltage, which you can generate with an oscillator.
Google that part number along with some keywords like effects pedal and you may find some complete designs. Also try the LM13600, which is the slightly older version, and "OTA" (operational transconductance amplifier), which describes its function.
You can get the data sheet at http://www.ti.com/lit/ds/symlink/lm13700.pdf
. The data sheet includes some designs you may find useful. It's not hard to do the 100% amplitude modulation with a square wave oscillator to make the stutter effect. It does use a split power supply (positive and negative supply rails) but can be biased for single-supply operation.
Check out this related thread: https://www.electronicspoint.com/threads/4047-4066-audio-slicer-help.254416/