Is wireless technology only possible due to inductance?
The cables aren't coiled. The current's direct. There's no inductance here.

That's not true, there's always some inductance, one millimeter of conductor has roughly 1nH of inductance. You cannot avoid it. The conductor can be a wire, PCB track, metal track on an IC, anything that can conduct electricity. There is always inductance.

The question is: when is that inductance significant? That depends on the frequency (rate of change) of the signal through the wire.

Electricity by itself doesn't mean there is an electric field and/or a magnetic field.

An Electric field exists as a result of applying a voltage between separated conductors, for example 2 plates. Like in a capacitor. The current can be zero. The voltage cannot be zero otherwise the Electric field would be zero as well.

A Magnetic field exists as a result of current flowing through an inductor, for example a current flowing through a wire. The voltage can be zero (but you'd need a super conducting wire for that) but the current cannot.

With an antenna you generally want to receive and/or transmit information, then a static field (one that doesn't change over time) is useless, you want to change the field(s) to transfer your information.

To change the field in a capacitor or around a wire, the voltage and/or current must be changed (modulated) that results in current flowing through a capacitor (to change the voltage, you charge/discharge the capacitor). Similarly for a wire or inductor the current must be changed and that can be done by changing the voltage.

So capacitance and inductance have a similar relation to each other as electric fields and magnetic fields do. There is no one OR the other all are related and cannot be considered on their own.

Wireless communications use Electro Magnetic Waves which have an electrical and a magnetic component. Most Antennas are electrical antennas meaning they mainly work with the E (electric) part of the field, example: the cellular antennas in your phone.

There are also "loop" antennas which mainly work with the M (magnetic) part of the field, example: wireless charging (of phones) and NFC (ID cards etc).

It depends on the application what is more convenient.