I thought 'Dao' was the pronounciation of 'Tao'.
Similarly 'kung' or 'gung' was the pronounciation of 'gong'. And 'Chi' is spelt 'Qi'. Hence sometimes seen as Qi-gong, pronounced as Chi-kung.
The official Pin Yin writing is relatively recent. Before that there was not much concensus in how to write chinese words in English. Although a lot of martial art terminolgy has more concensus probably due to its high media exposure, it still had to be corrected. So Qi is the official chinese way of writing chi i.e. Pin Yin. The reason for the overhaul can be explained in one example. Ji (pin yin) sounds like chi which will can confuse people especially because the meanings are so simular. i.e. the transliteration is energy for both words. The difference lies in the sub texts of the charactor relating to the adjacent charactor.
Unfortunately not everyone (including myself) is up on the official Pin Yin so we often use the unofficial writing even in published books, although that is getting rarer.