Let's take for example an electric eel applying an electric shock by creating a potential difference across two points in the water. It would seem, however, that the current would find a "shorter path" across the potential difference by just passing through the water. Why, then, does some of the current go through the "target" which is further away and likely has higher resistance than sea water?
Because the water is not a superconductor. You can model a sea water as a ladder of resistors put in parallel from/to infinity. Now if you apply the voltage difference between two points, the majority of the current will pass at the shortest way, the remaining arround. But exactly how much is a function of the resistance/conductivity of the water. More conductive, then the current cone to the sea bottom would be narrower. Less conductive water, then the current spread would be wider.
Electric eels tend to curl around the prey when hunting (and shock the predators when these make contact), so the shortest path for the discharge may well be though the prey's body rather than surrounding water.
Source: phys.org Credit: Kenneth Catania
Additionally, electric eels are fresh water animals, so your assumption about water being more conductive doesn't really hold. Blood and lymph are better conductors thanks to the ions (mainly Na\$^+\$ and Cl\$^-\$) present in them. In the end, a significant portion of the current will go through the body, which is enough to stun the prey or scare away predators.
Current takes all available paths simultaneously
... in proportion to their conductivity. (conductivity is 1/resistance, and its basic unit is the Siemens. A 100 ohm resistor has 0.01 Siemens of conductivity. Paralleling resistors now gets a lot more simple, you are now simply adding each of their Siemens and turning that back into Ohms.)
If that were not so, your house would never get any power - all of it would go to the steel mill, shopping mall or datacenter across the street.
This is how cows get killed by lightning that struck a tree nearby. Several megavolts at the tree radiate into the earth, creating a voltage gradient of say, 600 volts per metre. That puts about 1000 volts between their front hooves and their rear hooves. Some tiny amount of lightning current also travels through the cow, killing them.
Having two different resistances in parallel does NOT mean that there is no current going through the bigger resistance. The currents just divide: i1/i2 = R2/R1 (current divider).
If one of the resitances is, however, much higher than the other one the current through the higher resistance will beocme very small.
Obviously the resistance of victims of electric eels is not high enough compared to that of the surrounding water.