Strictly speaking, if you do a little Dr Who play/video for a group, or distribution, even non-profit, the BBC are within their rights to threaten to sue those responsible for driving the project.
Occasionally a local group will do a special one-night of a West End show, totally for fun/charity, only for them to be threatened with legal action.
Generally, organisations turn a blind eye to small one-off events, but this was far, far too well produced and the BBC jumped on it.
Even non-profit the organisers MUST consult the owners of the rights of the various aspects/trade marks & copyrights before even *considering* such a production. They didn't.
Put simple... Remember FOX paid a huge figure for the American+ rights to the McGann film, according to the organisers behind this, FOX could have made it non-profit and therefore saves on rights costs !!!!! I don't think so, given the potential profits drivers and by-product spin offs that may come from it !