Proper training and analytics in eSports require accurately collected and annotated data. Most eSports research focuses exclusively on in-game data analysis, and there is a lack of prior work involving eSports athletes' psychophysiological data. In this paper, we present a dataset collected from professional and amateur teams in 22 matches in League of Legends video game with more than 40 hours of recordings. Recorded data include the players' physiological activity, e.g. movements, pulse, saccades, obtained from various sensors, self-reported aftermatch survey, and in-game data. An important feature of the dataset is simultaneous data collection from five players, which facilitates the analysis of sensor data on a team level. Upon the collection of dataset we carried out its validation. In particular, we demonstrate that stress and concentration levels for professional players are less correlated, meaning more independent playstyle. Also, we show that the absence of team communication does not affect the professional players as much as amateur ones. To investigate other possible use cases of the dataset, we have trained classical machine learning algorithms for skill prediction and player re-identification using 3-minute sessions of sensor data. Best models achieved 0.856 and 0.521 (0.10 for a chance level) accuracy scores on a validation set for skill prediction and player re-id problems, respectively. The dataset is available at https://github.com/smerdov/eSports Sensors Dataset.