Playing the games simultaneously is actually innovative in how it let's them learn faster. If you play one game at a time consecutive moves are highly correlated which makes it difficult to make learning updates after each move. If you're playing 1250 parallel games that are starting and restarting so that they're at all at different stages of play, you can do an update after every move in every game and make better progress faster. This is known as Asynchronous Advantage Actor-Critic (A3C) and is a highly cited method discovered by the DeepMind team [1].
Surface Pro 4 - You'll get 6-8 hours of battery if you optimize some settings, and it's 12". I have no issues being productive on the type cover (I'm sure it can't be worse than a keyboard on an 8" laptop).
[1] https://arxiv.org/abs/1602.01783