... in... 1906 and largely before people drove everywhere.
Again, while I don't have the gene for sport, rail travel to Twickenham for the rugby has been a thing since whenever and presumably still is - people travelling to it do think of the stadium as about a half mile from the station - which it is, especially in wishful thinking terms.
The half mile separation is possibly useful to the railway as it must spread people out. It's been some time since I lived nearby - when the 1950s station's additional platform(s?) that served the stadium were very much part of things. Twickenham station's been much redeveloped though, curiously the current map at the National Rail site has those platforms (with track too...).
https://images.nationalrail.co.uk/e8xgegruud3g/31Q3CCYZjptJAnZfnHUfEX/c7f4a8a02538d2eaa357506ff8f917ec/Twickenham_station_map.jpgTravellers for the rugby also visit Twickenham town centre which is in the opposite direction, and I recall a work colleague from a workplace 100 miles away remarking that he always associated a match at Twickenham with the smell of sawn softwood as he walked past Alsfords the timber merchants in Heath Road. Puzzling as Alsfords *definitely* isn't in the direction of the stadium or station...
Mark
https://maps.nls.uk/geo/explore/#zoom=18.0&lat=51.45061&lon=-0.33047&layers=170&b=20