I think this is reasonable, but for consistency the same should apply to the B3021 at the S end (and to Albert Road at least in the Great Park): both are adopted roads with a highway corridor not part of HM's private park. From memory there aren't any obvious pedestrian crossings (perhaps in deference to Liz). This Mapillary photo (https://www.mapillary.com/app/?pKey=qc_Bwfxzzrvw7JWMS5_nDg&focus=photo&lat=51.46990805555556&lng=-0.6052580555555556&z=17) shows that park regulations are repeated either side of Albert Road where it crosses The Long Walk. I'd anticipate the situation is similar in the Home Park.

I only have recent photos of the A332 in the Great Park, which is more a road in a park rather than a road bisecting a park.