this one is not easily ansered in short. But I try:
The basic building block of a mcu is a "Logic Gate". These come in differrent flavours: AND / OR / NOT / XOR etc. see https://en.wikipedia.org/wiki/Logic_gate. The other one is a Memory cell.
Depending on the technique your cpu uses these can be build with transistors / mosfets etc.
For simplicity just imagine an AND gate to be one PNP transistor whose EMITTER only becomes high when there is current applied to both BASE and COLLECTOR.
Now to your program:
Your first instruction is sub which subtracts one value from another. If both values are the same, the target register only contains zero. So (for a 8-bit register) there are 8 memory cells containing zeros or which "don't contain current" / are "connected to ground".
Now using the logic gates you can OR these memory cells and end up with one output which is either high (if any of them is high) or low (if all of them are low.) This value is transfered (say connect output of this "wire" to input of memory cell) to the status register as Z-Bit.
Now to your second instruction: The conditional jump.
First the condition: This could be just one other gate which connects to Z-Bit memory cell.
Now the jump: The instruction pointer of your cpu is just another memory cell. But all we need is transfer the value of your jump target to that memory cell using some AND-gates.
So that's it?
Not really. It is much more complicated. We haven't talked about clocks, ALUs and much more stuff. But this should be the very basic operations so that you can imagine something which is at least not completely wrong ;)
EDIT: If you want to know more or just to prove that it is not so much more complicated have a look at this: https://hackaday.io/project/665-4-bit-computer-built-from-discrete-transistors