Very short range indoor RF transmitter - receiver circuits
I am still wondering if that is physically possible to make it work
for very short distances like in my bench and without the requirement
of large and complex antennas

A short monopole will work fine if you have a half decent earth. Alternatively, a short dipole will work at either end of the link. At circa 6.8 MHz, the wavelength is about 44 metres and a quarter wave monopole will have a natural length of about 11 metres but, if you shorten it, it will still work but, with certain provisos: -

The radiation resistance will be around an ohm or less when shortened significantly
The resistive losses will be more than the radiation resistance
The effective impedance of the antenna will appear highly capacitive.

To understand what I'm saying consider this graph: -

If you look along the x-axis at 0.25, the y-graphs indicate the resistive and reactive impedances of the monopole when used at a quarter wavelength. The radiation resistance is about 37 ohms and the reactance is nearly 0 ohms. This is regarded classically as the optimum length and corresponds to 11 metres at 6.8 MHz.
If you made a monopole that was one-fifth the length (2.2 metres) the radiation resistance will be an ohm (or thereabouts) but the antenna will look capacitive around 1000 ohms.
So, to get any power into a resistor of circa 1 ohm you need to: -

cancel the capacitive reactance with a series inductor
use an efficient impedance match to take your output drive (possibly 50 ohm) down to about an ohm.

At these sorts of frequencies you are probably going to choose a step-down transformer and a series inductor for capacitive reactance cancellation. You will have to live with the antenna losses (about the same value as the radiation resistance).
The same theory applies at both ends; receiver and transmitter.
Here's a calculator you can use to estimate the radiation resistance, reactance and antenna efficiency.
Good luck and make sure you are only emitting sub milliwatts or you might get a knock on the door from the neighbours or even worse, the authorities.