Sure! Here's a basic implementation of the game you described using HTML and JavaScript:
Save the above code in a file with a .html extension and you should be able to open it in a browser to play the game. The game will appear as a square grid, with blue circles representing runners and red circles representing taggers. The runners will move randomly within the grid, and the taggers will chase after them. If a tagger collides with a runner, the runner becomes a tagger and the tagger becomes a runner. There is a 1-minute timer, and if the time runs out, the game ends with an alert message.
Please note that this is a basic implementation and can be further enhanced with added features and graphics.