If you have recently purchased a game via Steam, you might want to continue downloading the game even while you’re playing other games. By default, Steam pauses downloading as soon as you start a game, here’s a workaround.
Continue Steam Download While You Play Games

The workaround is really simple. In short all you have to do is to ALT+Tab and unpause the download.

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Let’s say you’re downloading the latest Need for Speed: Hot Pursuit (Download Need for Speed Hot Pursuit Theme), which is nearly 8GB big.

1. Step Start the game that you want to play
2. Step Hit ALT+Tab to minimize the game (yes, not all games support this)
3. Step At the bottom click on “1 game paused” or go to your Library, then click on Downloads and you get this screen:

Steam download suspended while playing

4. Step Don’t click on Resume all, instead click on the Pause icon

Steam pause game download

5. Step Now, click on Resume again and Steam will continue to download your game

Resume Steam Download While you Play

6. Step Next, switch to your opened game and continue playing as you normally would

Just a little workaround. Maybe Valve will add an option to the Steam setting that will allow us to continue game downloads while we play in the future. It would make sense to me, because if you are downloading multiple games, it’s pretty annoying to do this for all games.

Anyway, background downloads will slow down your connection, so preferably continue to play some singleplayer offline games while you download Steam games.