Before AlphaGo, DeepMind released a reinforcement learning algorithm that could play many Atari games just from the raw pixels on the screen, in many games surpassing humans. The same algorithm.
https://arxiv.org/pdf/1312.5602.pdf
Reinforcement learning is a general framework for learning behavior from acting in an environment with the purpose to maximize a reward. It can be used, and was used, in multiple domains. AlphaGo used RL as well.
Saying that AlphaGo is limited because it only knows to play one game, is like saying that humans are limited because Lee Sedol could only master at world level one game. In fact, if the software was set to learn more games, it could learn them in addition to Go.
Also, regarding other tasks: a neural net that recognizes cats can be easily made to recognize dogs too. A program that translates English to French can be made to translate other languages too. We limit software to specific domains only on account of efficiency, not because algorithms are fundamentally limited.
Recently there has been a paper "Learning without forgetting" (http://arxiv.org/abs/1606.09282v2) that underlines this very ability to span multiple domains and adapt easily to unseen tasks and data.
> Developing a program that can generate solutions for a single specific niche of problems (while impressive) is not a convincing demonstration of intelligence.
Saying that people can do many tasks is not exactly right because a particular person can only do a few tasks, those tasks she was trained to do. If I never learned German, I don't know German. That doesn't mean the brain itself is limited. AlphaGo was only trained on Go, and its internal architecture was optimized for this one task in order to make it more efficient, but the method is general and reusable. DeepMind said so themselves, the breakthrough is not that they beat Lee Sedol, but that they used a general method that can be used to do other tasks as well. It is not a limitation of AI that we generally make systems that are good at only one thing.
If there is a limitation in AlphaGo, it is that it mastered a game where the whole situation is perfectly known (the Go board), while in reality many tasks are only partially known (such as card games, for example) so there is an extra uncertainty. But DeepMind and other researchers are working on that too.