Your game should only have a single activity and intent.
Some apps may have multiple intents. For example, you may open a map application to run it, or you may use it for navigation, or you may want to open a street view. That would be three intents for a single application.
For playing a game you really have only one intent. A user won't probably say "I want to look up my address book contact using this game", or say "I want to open this pdf file using the game", or "I want to navigate to an address using the game". Those would be different intents for the application. They almost never apply to games.
If you decide to use a splash screen (deep sigh, see Strategy's post) then it should be as part of your game. Although I detest splash screens, I do understand that they are sometimes there for corporate branding requirements, and other times they are useful to hide the fact that you are loading resources. In the second case they are a necessary evil.
Whatever your reason for it, your splash screen should simply be your initial game state. You start in the "showing splash screen" state. Then when the time expires you transition to your main menu state.
On the other hand..... If you did decide to make your splash screen into its own application with its own intent, it will be blissfully easy to swap it out with a non-splash-screen empty app. So in that case your users might be happy for your action since it means they can trivially bypass or remove your splash screen.