If the Bitcoin rig isn't free then the villagers don't get shit for years while it gets paid off. Then they're just sharecropping Bitcoin.
They could invite outside miners to set up shop in the village.
The miners would finance provide the capital, set up the mining rigs, and take all the bitcoin risk. The villagers would just sell them electricity. Just like they would sell electricity to any other business.
No clue whether that's what's happening in Bhutan, but it's a perfectly valid business plan, and pays the villagers right away.
It doesn't make any fiscal sense to find some out of the way location with a small scale hydro generator to set up a Bitcoin miner. The amount the village would need to charge to make a worthwhile amount of money will certainly be above large scale utility rates.
The Bitcoin miner in remote African village story smells like someone taking advantage of some villagers. They're either paying them below market rate for electricity or indenting them with a Bitcoin mining setup that will barely pay for itself over years.
If virtually no one else would buy the stranded electricity, the market rate would be zero otherwise. Anything more than zero is better for them.
There's more than one bitcoin miner in the world, so the villagers could get some competitive bids.
Why would it need to be free? It could be an ordinary investment that's paid off over time. (Though I assume that the payback period is probably quicker than 5 years, that seems a bit too long to be useful.)
Be careful about cows: there's quite a few charities who want to give out cows to help people (using the same logic as you do). But for many recipients the cow is a net drain on their resources. That same logic applies when buying a cow with your own money.