I'm afraid the picture that you have just gave does not work, could you make sure the image works? If you can't install it because it shows a grey button (unable to click it) It means you either never launched Half-Life once, or you don't have half-life at all, or hell, not even steam
1) Do you have enough free room on your hard disk to install ESF?
2) What game did you register with Steam? You will need to have Half-Life 1 (not Half-Life: Source and not Half-Life 2) installed, but it will also work if you have Counter Strike 1.6 installed, but ONLY if you bought CS 1.6. If you downloaded CS 1.6 through Steam, it will not work. It will only work if you have a bought version of Half-Life 1, or Counter Strike 1.6.
3) If you have Half-Life 1 installed, you will need to start it up at least one time, and do one level (you do not have to complete the level: just start it up. You can then exit it). This creates the folders and files that ESF needs in order to run. If you do not run Half-Life once, it will not work. I don't know if the same goes for Counter Strike 1.6, but it couldn't hurt to try if you have CS 1.6.