In this circuit the role of decoupling caps is to reduce power supply impedance.
A transistor wired as an emitter follower, as is the case here, can turn into an involuntary Clapp/Colpitts oscillator when collector impedance is inductive enough (due to long traces to the nearest decoupling cap) and layout parasitics (inductance/capacitance/coupling) adds enough of the wrong kind of feedback.
Having a capacitive load (in this case, a cable) makes things worse, although the 10R emitter resistors should be high enough to mitigate this.
Basically, suppose an emitter follower driving a load of impedance \$ Z_L \$ with a signal of amplitude \$ A \$ applied to the base. Suppose the emitter follower is ideal, thus the signal of amplitude \$ A \$ is present at the emitter. Thus emitter current into the load is \$ A /Z_L \$ , collector current is the same (neglecting base current). If its power supply at the collector has an impedance \$ Z_S \$ then AC voltage at the collector will be \$ -A Z_S/Z_L \$ ...
If \$ Z_L = 1/jCw \$ (capacitive) and \$ Z_S = jLw \$ (inductive) then AC voltage at the collector will be \$ A L C w^2 \$
Notice that since \$ j^2 = -1 \$ the sign flipped, basically the capacitive load and the inductive supply both add \$ \pi/2 \$ phase shift.
This means the signal on the collector due to the inductive power supply impedance has the same polarity as the input signal.
With the "right" conditions this can create positive feedback to the base, and your transistor will oscillate. An inductive power supply can also create LC resonances with the transistor's internal capacitance.
An illustration of this problem is attempting to repair an old amplifier where the output transistors are screwed on a heat sink and connected to the PCB via rather long wires, as was often done back in the day. This worked well with old, slow power transistors because their high frequency gain was low. But if you replace them with modern faster transistors, or even worse MOSFETs, which have gain up to much higher frequency, the wire inductance will may make them oscillate and they will blow.
So the decoupling caps are not really related to load inductance, but to supply impedance.
Note that modern 100µF caps with decent low ESR (a few ohms) and 2.5mm-5mm pin spacing have only a few nH stray inductance. If you don't have a ground plane, this is the same inductance as a bit of trace of the same length as the current path through the cap. And a 100nF thru hole cap having the same pin spacing as the electrolytic has the same inductance (but lower ESR). Thus, for this circuit, the 100nF ceramic caps would only lower power supply inductive impedance if they are much closer to the transistors than the electrolytics.