Ran in an area that doesn't appear to be in a city / has no "roads"

I ran in Lake Geneva, WI over the weekend and there appears to be an area on the south side of the lake that has no “roads” or “nodes” and is not in a designated city?

Is it outside of the city’s very odd borders? Lake Geneva, Wisconsin - CityStrides

Yes, appears to be! Not sure if its maybe not in a designated city? No worries, was just curious! Thanks for the quick response!

I searched around trying to figure out which city it belongs to, within OSM, and I haven’t been able to figure it out.
Maybe someone else reading along can help us find the missing city

This link could help. I am guessing it’s a village if its outside the city limits