From ‘cupboard’, a chair is taken out?

Solution 1:

In British English, a cupboard can be either a free-standing piece of furniture or built-in. The one referred to by Milne is obviously a walk-in cupboard, which presumably must have been mentioned somewhere in the stage directions. The date of the play is not relevant; there has been no 'change in meaning'.

Solution 2:

In Australian English the generic term would be "storage space", not "storage room".

A storage room is a room, i.e. an inside space which is large enough to walk around in and used for storage. A room may be small, for example a toilet.

A cupboard is different from a storage room because it is not intended to be occupied. A built-in cupboard may have the same floor as the house and appear on house plans to be similar to a very small room, but it is not designed for occupancy and there is usually no light, ventilation or an interior door handle. Access to such a cupboard is usually through a person standing in its doorway. Other built-in cupboards, such as those built under a bench, cannot be entered easily.

Some cupboards are free-standing units, used for storage. If such a cupboard were large enough, it could contain a chair or a person. The word is also used for the closable part of a storage unit, built-in or free-standing, which is partly closable and partly open.

Some words may refer to cupboards or to other spaces. A pantry may be a cupboard, but in some older houses it is a room containing food storage cupboards. In a caravan it may be a shelf. Some modern houses have a "walk-in pantry", which has shelves and enough floor space to allow access to the shelves. Such a pantry would not be referred to as a cupboard. Similarly a "walk-in-robe" serves the function of a wardrobe for storing clothes, but allows access for a person within the space. The clothes themselves may be on open spaces or closed spaces (cupboards) within the "walk-in-robe".

In my experience, the essential features of a cupboard are that it is intended for storage, closable with a door, and not designed to be occupied.