Let's have a look at how SpriteBatch works:
SpriteBatch draws sprites onto a 2D plane. So if you had wanted to rotate your sprites so that they come "off" this 2D plane, then you'd probably have to find another solution. But, looking at your video, it looks like you want to rotate the entire 2D plane.
SpriteBatch's normal mode of operation uses a built-in orthographic projection matrix into client space. It also lets you pass in an optional global transformation matrix. You could use this global transformation to get your effect, but you'd also have to "pre-undo" the projection matrix that comes afterwards, and the maths is annoying.
But fear not -
SpriteBatch has another mode of operation, where it can use any
Effect, using that effect's vertex shader and transformation matrices.
BasicEffect will do nicely here. Take a look at this article to get the basic principles.
BasicEffect.Projection matrix to a suitable perspective projection. And then set
BasicEffect.World matrix so that your plane of sprites appears in the correct location (and the right way up!).
Take a look at this article as well. It describes the process in more detail.