Why doesn't all current flow to ground but instead splits into 2 paths (as shown in the schematic)?
First, currents don't flow to any particular location, instead they establish complete circular flows.   A single-point ground is irrelevant because it lacks a complete circuit.  

To understand this circuit, erase the ground, then analyze as usual.


  I've learnt that "current will flow through the path of least resistance,"


Learnt where?

:)

"Path of least resistance" is a widespread physics-misconception; almost completely[1] bogus.  It doesn't appear in science texts, instead it's something repeated in news articles written by non-techies.   As you've discovered above, it's just not true.

It blatantly violates Ohm's law.

How can we stamp out "path of least resistance" and other similar electricity-misconceptions?  These mistakes spread from mind to mind like a rumor, or like a "disease."  They tend to infect little kids before they had a chance to learn any real physics.   (Heh, so how many other similar physics-mistakes do we all believe right this minute?)

Maybe we can fight fire with fire.  Lets replace "path of least resistance" with an improved version.  For example, here are a couple of semi-correct rules for electricity behavior:


The greater the pressure-difference, the faster the flow.
Increasing the resistance will decrease the flow.


These are two re-statements of Ohm's law for wires of fixed diameter.  If the wire AWG stays the same, then a higher current is a faster flow of charge.

.



[1] ALMOST, because incoming lightning can be diverted from high-resistance paths using grounded conductors.  But lightning is neither electricity nor current; lightning is a progressive avalanche effect; a gas discharge, same as neon signs and Aurora.  Lightning is more like a growing fracture than  an electric current.  Second, if power supplies have high source-impedances, then suddenly attaching low-resistance load can greatly lower their output voltage.  (Obviously that's how lightning rods function.  They rely on a lightning channel having a fairly significant resistance.)

Perhaps the mistake starts with observations of water: the growing end of a new stream will usually take a single path as it grows downhill.  In some cases electric currents act like water.  But since there's is no closed hydraulic circuit present, the growing water-stream is a false and misleading model for electrical behavior.