Short positions are closed when a stock is delisted. It looks just like a normal 'buy' at the last known price which then zeros out the held shares. The wording in the documentation may be a bit misleading. It's correct that one will typically profit on a short position when the security is delisted. However, there are a number of reasons why a stock can be delisted (eg a merger, going private, failed to file required statements, etc). Not all of them result in a lower price. Mergers and going private, for instance, often result in a higher price which one would loose if the security was held short.
See attached algo. Look at the 'Daily Positions and Gains' report. Note that on 8-1-2018 the short position of IMNP was closed at a profit.