Simon Kuznets only came up with the GDP in the 1930's and he was not particularly happy with the measure he created. GDP for any time before that, therefore, is more of an estimate as economists need to reverse engineer what they can from census data and similar statistical information.
German GDP in 1913 is established as by Myszczyszyn in 'Use of ...
You said that you could only find the answer in 1960 US dollars. I found a site (https://www.usinflationcalculator.com/) that gives us the value of a 1960 dollar compared to 2020 (866%) so you should be able to find the value by simply multiplying it by 8.66. You might want to double-check me though.
We seem to look at two questions quite different from another: "why was the Weimar Republic founded" and "what does the author of that podcast mean with his statement"?
This answer assumes that the second of those is in this context the more important question, the first being for this purpose 'adequately' addressed by Wikipedia: Weimar_Republic#History.
What was the purpose of creating the Weimar Republic? (Podcat) speaker said The Weimar Republic was created so that it could take the blame of Germany's defeat in World War I. But how can that be if the Republic was founded a couple days before the end of WW1?
Without knowing exactly what this podcast is proposing, one can make ...