TL;DR In the DQN paper, each environment was trained for 50 million frames, grouped in fours without overlap, so there were 12.5 million state, action, reward next-state records used.
The above direct numerical answer to the question as posed is not the whole story though.
I'm trying to understand the dataset and how many states, actions and rewards have been used to train the agent on a single game.
It seems you are viewing Reinforcement Learning (RL) through terms you understand from supervised learning. Although there are some similarities, especially when considering the neural network that performs function approximation inside most deep RL, there are important differences which mean the information you are looking for doesn't really exist.
The main purpose of RL is for an agent to learn through experience that it also helps to generate, through trial and error. Although off-policy algorithms such as DQN could learn from fixed datasets (and there are some circumstances where they might, perhaps as part of a more complex pipeline), this is not what the papers you reference are doing.
RL experiments can be repeated provided all random number generators (in the learning agent and in the environment) are seeded the same way. That may be of interest to researchers wanting to replicate work exactly, but more generally useful are statistical measures of "typical" learning graphs. The environment defines the problem to be solved, and the exact data generated through the RL agent exploring it in a set of runs is not necessarily as interesting when interpreting the results, or considering whether to use a certain type of agent for a specific problem. Having a reference copy of the environment identical to the one used in the paper is the equivalent in RL of having the "dataset".
You could log the state, action, rewards data from each experiment (and in DQN it is already being stored temporarily in the experience replay table), but you would not expect it to repeat on the next run even with the same agent. Also, when comparing to some other agent (or agent hyperparameters), one major point of difference is that you would expect that agent to generate a different set of states, actions and rewards - choosing how and when to explore different parts of the environment is a key differentator between agents. So it is usually not considered a critical part of the work to log every state. That's not to say that researchers won't do it - presumably many do keep records for debugging or simply to be thorough. However, more important in published RL results is to characterise the learning curves against some metric such as the amount of experience required, or another cost such as total CPU resource or time used in training.
In the original DQN paper, I believe that each 4 frames were stacked separately into a single state, without overlap, thus each 4 frames equals one state, for which a single action would be taken and then reward and next state observed. So dividing the frame count by 4 should give you the "dataset size". But it is important to note that this was never used as a whole in a supervised learning manner, and was not re-used between runs. The experience replay buffer was sampled randomly on each timestep, and there was an average number of times each sample was used (32 I think) to train the network - you might compare that to running 32 epochs of training across all state/action pairs as inputs, but it is only a loose comparison due to the sample-with-replacement sampling strategy and the sliding window effect of the experience replay.
