I like the answer just above.
I think that Dan is a little confused by the trains.
There are two stations in Windsor, served by different companies and going to different parts of London.
The station directly opposite the castle is Windsor & Eton Central as mentioned in the OP. But it is Great Western trains (GWR) and does go into Paddington station with a cross platform change at Slough heading towards Windsor and a staircase and an up and over at Slough leaving Windsor.
The other station is down the hill and around the castle walls and down to the river and is called Windsor & Eton Riverside. It is the end of a branch - a slow branch - from the South Western Railway (SWR) mainline from London Waterloo. Much slower and a little more expensive than the GWR route, but with no changes on the way.
The tickets are not interchangeable between the two routes.
As said above, a good choice in this case is walk down the hill and take the SWR train from Windsor & Eton Riverside to Waterloo and walk the reasonable distance along the South Bank to the theatre.