Technically, this price hike isn't due to Bitcoin at all, but rather some other, newer cryptocurrencies like Ethereum. Using GPUs to mine Bitcoin hasn't been profitable for years, since specialized mining hardware came out that was far more efficient at the task, making GPU mining of Bitcoin obsolete.
These newer currencies are designed to make it difficult to use that kind of specialized hardware, so at least for the time being, graphics cards are what gets used. The GPUs perform complex cryptographic computations, the results of which are chains of numbers, which are all the generated money is. As more currency gets mined, it becomes computationally harder to mine additional currency, resulting in a limited pool of money.
Since the cost of electricity factors into how much profit can potentially be made, a mining system will typically have multiple cards installed to reduce the overhead of other components. And some larger-scale operations will be running many of these multi-GPU systems, basically like a money-factory. And this is where a lot of the GPUs go.
Since the production of graphics cards is limited by what the manufacturers expected to be selling for normal purposes months ago, the supply of upper-mid range cards has become limited, since those are the cards that tend to offer the best efficiency in terms of profit over operational costs. And the card manufacturers don't necessarily want to ramp up production either, since these alternative currency markets can be volatile, and if mining with these GPUs becomes unprofitable in a couple months, there will be a ton of cheap cards available on the secondhand market, making it hard for manufacturers to offload all the additional cards they would have made.