The Whitworth was developed pre-war by Joseph Whitworth of England. He found that the P-53 had inconsistent bore sizes (worn out cutting bit) that does not endear it to accuracy. He decided to make a more precise gun with precision but bores and bullets to match. While outwardly appearing to be like an Enfield rifle musket, his gun was more accurate. Besides being more precisely made, the smaller diameter .451 bullet has a superior ballistic coefficient than the .577 Enfield. This meant it could buck the wind better and was lest liable to drift because of the wind. Additionally, the bolt (as the Whitworth bullets were called) were propelled by 70 grains of powder (as opposed to the 60-65 grains for the .577 Enfield). However, the smaller bore Whitworth fouled easily and was not deemed desirable for general issue as an infantry arm in England. Some British regiments received some, but only on a limited scale.
So, to answer the question, the Whitworth was not a target gun per se. However, because it was one of the most accurate guns of its time, it was used by the target crowd in England.
Whitworth rifles are displayed and may be seen at Gettsyburg, Chickamauga, Virginia Historical Society (Richmond, VA), 45th Infantry Division Museum.
BTW, buy yourself a back-issue of The Gun Report that has John Gross's article. It's worth it.