From what I see in this picture it looks like the building being demolished is either the 'Engine Fitting Shop' or 'Pattern Store' as what I have researched and seen (when going on the Dockyard walk's dueing the Herritage Weekend, aswell as when I have walked around Bluetown),the 'Dockyard Pump House' is still there and is now either the 'Lappel Office'or the 'Fruit Office', along with the 'Shipwrights Machine Shop'that was Previously the 'Working Mast House'.
If I am wrong about 'Dockyard Pump House' I would like to know what this building is (if known)