The energy release you witnessed was not actually due to the ropes being twisted. It was due to the child on the seat being lifted higher as the combined rope length shortened. Basically
gravitational potential energy.
Ep = mgh
Thus a 30kg child lifted 20cm higher (due to the twisting of the ropes making them shorter) now has potential energy of:
Ep = 30 * 9.8 * 0.2
Ep = 58.8 J
Ep = 58.8/3,600,000 kWh
Ep = 0.000016333 kWh
So assuming you pay $0.30/kWh for electricity, the amount of energy stored (and hence the absolute maximum amount of energy that could be harnessed upon release) would be worth:
Value = amount * unitValue
Value = 0.000016333 * 0.3
Value = $0.0000049
Value = 0.00049¢
The value of the energy produced would never recoup the cost of the rope (before it wears out), so it will never be economically viable. Sorry.
That's not to say the idea can't actually be used to do something useful. Just get a falling mass to power a generator and produce electricity (like this
https://gravitylight.org/how-it-works) and you can have an easy-to-construct and hard-to-break 'power supply' that can, in certain circumstances, be a quite satisfactory solution.
The thing that breaks your original idea is the failure rate for twisting ropes. If you replace twisting ropes with a rope over a pulley, then the rope lasts longer and your economic efficiency increases. If you replace ropes with steel cables and large diameter pulleys, it gets even better. If you instead have chains pulling a cart with rocks up a rail track on the side of a hill it gets even better. If you throw all that away and just use
solar power (generated during the day) to pump
water up a hill and into a reservoir, and then release that water at night through a turbine (when the PV panels aren't generating anything) to get the energy back, then you're pretty much at the point that we're at now (it's called 'pumped hydro'). All of them are essentially the same:
Use surplus energy at one point in time, to lift a mass (give it potential energy), then later release the mass and recapture some of that energy.
PS: Anyone lucky
enough to live in a hilly area with an elevated water tank (or the potential to install one) already has most of what they need to store renewable energy during the day and use it at night with a round-trip efficiency of over 60%...
https://en.wikipedia.org/wiki/Pico_hydro