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In order to actually play a game in GOG Galaxy 2.0, you need to:

1) Open one of the game listings (which might involve going back if you are looking at the page for a game already)
2) Open the game's page
3) Click on the "Play" button hidden all the way at the top of the screen.

or

1) Open one of the game listings
2) Right-click on a game
3) Hit play


Both of those seem rather needlessly long.

The fact that you can't see both the games list and the game description at the same time forces you to constantly go back and forth.
The fact that you have to open a game's page in order to play it makes it take far more clicks than it should, and it's made even worse by how far out of the way the play button is. You should be able to just double-click on a game's thumbnail to start it immediately, or there should be a play icon on/under/near each thumbnail to play directly without opening the page.

Others have already covered the lack of recent game entries in the tray icon context menu.
We have couple of ideas how to address that and they might be made possible in one of further updates. For now another option is to bookmark a gameview and double click it. This will also launch said game.

Other quick option is to right click on the recently played by me section title. With current update any game started through GOG Galaxy should show up there
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NamelessVoice: You should be able to just double-click on a game's thumbnail to start it immediately, or there should be a play icon on/under/near each thumbnail to play directly without opening the page.
+1
Would increase usability a lot for me!
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NamelessVoice: You should be able to just double-click on a game's thumbnail to start it immediately, or there should be a play icon on/under/near each thumbnail to play directly without opening the page.
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gadjuka: +1
Would increase usability a lot for me!
You can also right-click a game and select play.