Lining the different table of content items up vertically instead of horizontally is easy - just put them both on Rows instead of both on Columns. But for the rest of it, actions just don't really work that way. Filter actions happen based on the mark you select and the way the view is set up, you have two headers but actually one mark (that's why you see only one blue dot) You could maybe put the two fields on two separate worksheets and use something like this: Table of Contents Creation to Navigate to Other Dashboards | Tableau Software
I would also think about who your audience is, what you want them to get out of interacting with your dashboard/workbook - is it even necessary to start with a table of contents, or do you want to just start with the view of players and allow them to dig in and filter that? In that case, ou might actually be happier using parameters or using a regular filter.
The following articles from our product help explain a little about the differences between parameters, actions and filters and when each might be useful: