No, you don't need any other visa. You would not get one if you tried to apply for it.
On the other hand, your point of entry is indeed Germany, it's not even something that's a matter of interpretation. You will go through a passport check and get an entry there, at which point there is nothing physically stopping you from leaving the airport and driving through several countries if you want to. That's the way airport are setup everywhere in the Schengen area.
But allowing you to enter a country with a visa issued by another one is the whole point of the Schengen regulations (or at least one of its cornerstones). It's by no means mandatory to have a visa from every Schengen country you intend to visit (what would be the point of a common visa policy if it were the case?) nor even from the country you are entering first (as the rule is very clear: you have to apply to your main destination, not to the country of first entry).
In some very specific cases, showing up somewhere unexpected with a visa from another country can raise questions about the truthfulness of your application and your real intentions but in your situation, transiting through a major hub with a multiple-entry visa and a ticket to somewhere else, that's extremely unlikely to be a concern.