System classification: unit-time delay
You are right that a distributed system could be "something like a transmission line". Note that the system

$$y(t)=x(t-T)\tag{1}$$

is a simple model of a transmission line, where just a frequency-independent delay $T$ is taken into account, and the attenuation is neglected.

Note that lumped electrical systems, described by resistors, capacitors and inductors, result in ordinary differential equations, i.e., the output $y(t)$ depends on the time derivatives of the input and output signals. If the system is also time-invariant, i.e., the component properties do not change over time, you can define a transfer function, and with lumped elements that transfer function is always rational. The transfer function describing the system given in $(1)$ is

$$H(s)=e^{-sT}\tag{2}$$

which is clearly non-rational.