In old times there where several ways how work with yeast. Some where repitching their yeast on and on and got some really stable cultures (kveik), some of them where drying them on wood to prolong shelf live. Besides pitching it again and again you could also buy yeast in the 17th century from other breweries. So it is quite odd that Goslar still where fermenting their beer spontaneous without adding yeast. Here are some sources that state that Gose was produced without adding Yeast:
Since the beer was not inoculated, the fermentation happened by itself or a thick layer of mold developed. The thicker the leather like skin was the better the beer was keeping since the mold layer was keeping oxygen from getting into the beer.
The Goslarsche Gose inoculates itself without the addition of yeast or gest.
But was it completely spontaneous like Lambic today? I would say so, not completely, reasons for that are that it is fermented in cellars in wooden vessels. Even though the vessels where cleaned with hot spruce water  it was not enough to kill all yeast and bacteria that where present. Then it was transferred into spruce Barrels  which where also a good possible host for yeast. In conclusion, yes there is no additional yeast added but the yeast in the wood would be there to support a good fermentation. Another thing is that it was dunk fresh, modern knowledge absolutely recommends against trying a spontaneous fermented beer for the first 3 weeks. A lot of quite bad bacteria inhabit the wort before yeast and lactic acid bacteria take over and produce acid and ethanol to kill them off. In my clone I countered that with the addition of Lactic Acid and 2% Alcohol (via Vodka) in my wild starters.
If someone would produce historic Goslarsche Gose today he should decide, either spontaneous ferment and lager in barrels for a longer period of time and therefore let it sour. Or use a mixed culture with a strong Saccharomyces to ferment it and serve it quite fresh and not sour (under 3 weeks). I also speculate that using a culture like Kveik would not so far off the real culture that inhabited the wood. They brewed a maximum of 4 times a year in the cellar, the beer was transferred to wooden barrels only 1-2 days after brewing, so Brettanomyces would not have a chance to start fermenting at that point. It was starting to ferment in 24-48 hours which is quite fast for spontaneous fermentation. It was not getting sour, I would say due to hopping but maybe it was due to a fast acting Saccharomyces like the Kveik strains.
In conclusion we can say that the Gose was spontaneous ferment, but had a little help from yeast in the wood. Maybe this yeast was a Kveik like culture that ensured that the beer was drinkable.