How to determine if a signal path needs to be treated as a transmission line?
The boundary between lumped and distributed systems is not clear-cut but there are some commonly used values. For distributed systems transmission line theory is required.

The distinction is usually made based on the effective length of a signal or the feature of a signal like an edge. So it's important to consider the rise- and fall time of a signal and not the frequency. Nevertheless the frequency imposes an upper limit on the risetime.

In air a signal travels with about 85ps/in (~ 33ps/cm).
The propagation delay depends on the dielectric constant, it is proportional to the square root of it. For a PCB with a dielectric constant of 4 (like FR4 which is in the range of 3 to 5) the propagation delay doubles.

A rising edge with a risetime of 1ns would occupy a trace length of 1ns/(2*85ps) ~ 6in (~ 15cm). At the driving side the signal is already high when at a 6in distance it just starts to rise.

So a 6in (15cm) track clearly is too long, since the potential varies from low to high along the track. 

If the length of the track is between 1/6 or 1/4 of the effective length of a feature like an edge a system can be regarded as lumped.

So the upper limit for the example given above is between 6in / 6 (= 1 in, ~2.5cm) and 6in /4 (= 1.5in, ~4cm) for a trace on a PCB with a dielectric constant of 4.