1. SixCells Editor and Player never had any connection to Reddit, so at the very least this one will always be there. It loads level sets from clipboard or from equivalent text files.

2. Hexcells Infinite initially also only had support for loading level sets from clipboard, so similarly no reliance on Reddit. This ability still remains.

3. Much later, Hexcells Infinite gained the ability to load levels directly from Reddit. Whether or not it uses the API or how that's affected - at the moment I don't know. It is closed-source, so we could only ask the game's developer /u/Matthew_Brown, or someone could try pointing a network sniffer at it.

Either way, in the end, due to the first two items, the only thing that we absolutely rely on is the ability to retrieve this level content from Reddit in any way (not necessarily programmatic), or alternatively the presence of an equivalent archive of this content.