To store 1.2GWh (or 4.32TJ) of energy in a gravity battery that had a vertical drop of 450m in a gravitational field providing an acceleration of 8.9m/s2 (or so I assume... you've missed the power-of-two bit out of your question) you'd need a total weight of about 1.8 million tonnes.
If that mass were granite (density ~2.7g/cm3), it would have a volume of about 400000 cubic metres. If that were a cube, it would be about 73.7 metres to a side (~17-18 storeys tall). If you made the mass out of iron (density ~7.874g/cm3), it would have a volume of ~137000m3 (or a cube ~51.5m to a side).
Of course, that assumes you have the ability to perfectly convert the descent of the block to electrical power, and in practise that's going to be challenging and I'm assuming your peeps don't have ready access to room-temperature superconductors and the like.
Real-world gravity batteries have efficiencies of around 80-90%, but notably they use pumped liquids or vertical drops and so would not have the problem of friction losses over several hundred metres of track. I suspect the best thing to do would be to cut a shaft down from the top of the mountain, and the excavated material could be used as the working load of the battery.
You probably wouldn't want to drop the entire load down at once, but one (or a few) large lumps at a time to minimise the necessary strength of the infrastructure, or the destructive effects of an accident. With a descent of 1m/s, a load of about 3000 tonnes would provide you with the required 25MW power output. You'd need 600 of these blocks to provide power for the full two days. Down a 65% slope (~33 degrees) it'd be moving at about 1.8m/s to get the requisite downward velocity.
How tall and wide would this device be if they wanted it to be as narrow as possible?
Your question is under-constrained, because you haven't said what your peep's engineering capabilities are. Clearly, when dealing with thousands of tonnes of rock moving at a time, you can't really make things that small. A cube of granite that size is about 10 metres to a side. You'd want at least two of these, so as one brakes its load to a halt at the bottom the other can start going. Two 10-metres slides (or shafts) are probably wanted, with enough space at the top and bottom to move the loads out of the way ASAP. The fewer slides you have, and the narrower your system, the harder it will be to get the weights into place at the top and out of the way at the bottom, and that means more losses and more inefficiency. TANSTAAFL, etc.