Hello, aceman444! 

I changed the tags based on the data from the OSM Wiki at the link: https://wiki.openstreetmap.org/wiki/Tag:sport=motor It is said that the tag "highway=raceway" is more suitable for linear objects. Based on this article and the fact that the territory includes the racing area and building, I came to the conclusion that “leisure=sports_centre” is the more correct tag. 
But I didn't notice that the area is used for the show. I’m sorry for my carelessness and thank you for paying my attention to this.

I studied another article about raceways again (https://wiki.openstreetmap.org/wiki/Tag:highway=raceway ), where it says that small raceways can be mapped as a polygon with adding the tag “area=yes”, but the building should be excluded from this area. Another option for this area is using the tag “area:highway=raceway”. Both options require changing the geometry.
One more option that I see is using “tourism=attraction” for the area, it doesn’t require geometry changes, but it will be a cause of the duplication (there is such a point nearby).

So, in my opinion the best way is using the tag “area:highway=raceway” and fixing geometry.
What is the best way in your opinion?