Ah, I haven’t seen that page for landuse=fairground before since it is so new. I would say that that the example picture looks more like just a grassy area in a park (and I wouldn’t even tag it)
Compare this to something like the Wisconsin State Fair Park.
I also found the tag recreation_ground=showground (with similarly low usage). This appears to be the same thing as a fairground (in US English), so perhaps a showground would be the better term in any case. I’m not a fan of it requiring landuse=recreation_ground, given that a show/fairground is not “An open space for general recreation, which often includes formal or informal pitches, nets and other recreation equipment or infrastructure.”