First of all, I am kind of confused with your question. But I will try to answer with the best of my abilities. K-means clustering is an unsupervised clustering method based on the distance (typically Euclidean) of data from each other. Data points with similar features will have a closer distance, and will then be clustered into the same cluster.
I assume you are trying build an algorithm that outputs a recommended game, given an individuals concentration, response time, memorization, and attention skills.
The first problem is I cannot find a proper dataset that contains the skills and games.
For the data set, you can literally build your own that looks like this:
labels = [game]
features = [concentration, response time, memorization, attention]
Labels is a n by 1 vector, where n is the number of games. Features is a n by 4 vector, and each skill can have a range of 1 - 5, 5 being the highest. Then populate it with your favorite classic games.
For example, Tetris can be your first game, and you add it to your data set like this:
label = [Tetris]
features = [5, 2, 1, 4]
You need a lot of concentration and attention in tetris, but you don't need good response time because the blocks are slow and you don't need to memorize anything.
Then I am not sure about how to find out clusters.
You first have to determine which distance you want to use, e.g. Manhattan, Euclidean, etc. Then you need to decide on the number of clusters. The k-means algorithm is very simple, just watch the following video to learn it: https://www.youtube.com/watch?v=_aWzGGNrcic
Furthermore, how can I do it without a dataset (Without using reinforcement learning)?
This question makes 0 sense because first of all, if you have no data, how can you cluster them? Imagine your friends asking you to separate all the green apples and red apples apart. But they never gave you any apples... How can you possibly cluster them? It is impossible.
Second, I'm not sure what you mean by reinforcement learning in this case. Reinforcement learning is about an agent existing in an environment, and learning how to behave optimally in this environment to maximize its internal reward. For example, a human going into a casino and trying to make the most money. It has nothing to do with data sets.
