Electricity needs a loop because the electrons need to go somewhere after giving up their energy.

Just your water pipe idea, where a pump returns the water to the top flow down again, the electrons return to a battery, say, to be re-charged flow again.

In the voltage divider, the current flowing into Z1 then gets split and is shared across Z2 and the load at the output.

If the load current is much less than the current at Z2, it can be approximated as not being there (the beauty of engineering) and

Vout will equal Vin x Z2/(Z1 + Z2). (that's also why voltage dividers are not used as power source)

The current from Vin to Gnd is = Vin/(Z1 +Z2)

With the current known, then the voltage across each Z in known: V=current x resistance

and in total Vin = (current x Z1) + (current x Z2) with Vin = Vz1 + Vz2

With some algebraic substitions, this can be solved to yield Vout (or Vz2) = Vin Z2/(Z1 +Z2)