For any game that we both own on Steam, I don't see the option anywhere within the Steam client to invite someone on my Steam friends list to play a game with me. This is the only menu I see when I right-click my friend in my friend's list.
How can I invite a friend to my game using the Steam Client?
The game should support multiplayer and it will only usually let you invite a friend to play when you are in a suitable section of the game, such as a multiplayer lobby or a game that has an in-game option enabled that lets friends join you. If, for example, you are in the main menu of a game, it usually will not let you invite a friend (unless that main menu shows you in-game that you can invite friends).