This name is a synonym of Capillipedium spicigerum S.T.Blake.
The record derives from Tropicos
(data supplied on 2012-04-18)
which reports it as a synonym (record 50140271) with original publication details: Boissiera 9: 154 1960.
This name record (from Tropicos) was not included in version 1 of The Plant List. It is possible the same name was included from a different data source, to check this you can search for Capillipedium parviflorum in version 1 of The Plant List.