Ich denke das wir solten auf Englisch schreiben heir. So more can understand in case they have the same issue/question.
Okay, I see that you are getting the table view on the page you referenced above. That means that the taxonomy-teams.php is NOT getting called. (See the WordPress Template Hierarchy (http://codex.wordpress.org/Template_Hierarchy)
By inspecting your page (http://wp.vermins.de/teams/herren-landesliga/) I can see that the shortcode is being accessed because there are css elements like <table class="mstw-tr-table">. That makes it certain that [mstw-tr-roster] is lurking on the page that is being called. If you inspect http://shoalsummitsolutions.com/dev/teams/cal-bears/, the page that picture 6 came from, you'll see very different CSS elements.
(All assuming of course that you have not made HUGE modifications to the taxonomy-teams.php template to display a roster table rather than a player gallery.)
So maybe you can try this:
- Create a new team (with slug new-team, say) and create one new player on that team
Then just type http://wp.vermins.de/teams/new-team/ into your browser and see what happens.
Let me know how it goes.
P.S. Das "s" ist sehr interessant. "Vermin" comes from the Latin word for worm, "vermis", with a (nominative) plural of "vermes", so whatever! :-)