Western Skittles is a slightly misleading catch-all term encompassing all manner of subtly different games. Geographically, this category of skittles is played in a very wide area, including the West Country and across to the Cotswolds, South Wales and its English border counties, and even as far as Coventry. The common denominator is the use of nine skittles and three balls, bowled at speed down a (usually) wooden floored indoor alley. Needless to say, in these 'Western' areas, the game is known simply as Skittles (as indeed it is in every other area where skittles is played). Skittles is a big deal in the 'West', and there are numerous leagues, and almost as many different rules of play, which I have no intention of attempting to summarise here.
This good alley at the Village Inn, Twyning is typical of those in Gloucestershire. The pub team play in the local Tewkesbury & District League, which has a very useful map locator for the various venues in the league should you wish to visit and throw a few balls down yourself: http://www.tmsl.me.uk/