Chessclub `Promotie' (`Promotion') in Zoetermeer, the Netherlands has for many years each year between Christmas and New Years Eve an `Oliebollen'-tournament. (Oliebollen are a traditional Dutch treat for the end of the year. I do not know many foreigners who like them.) In this tournament, several chess variants are played - some existing ones, but also several new ones, just invented for the occasion.
In a booklet called `Bloemlezing Humorschaak', written by Henk Breugem of SV Promotie many of these variants are described. One of these is `Hoekveldschaak', or `Corner-square chess'. The variant is probably invented by Henk Breugem or another member of Chessclub `Promotie'.
Note: when a player has moved his king to a1 or a8, and then moved the king away, the right to take pieces is again cancelled, and returns only after the king is on a1 or a8.
The rules are not clear whether a king may take from square a1 or from a8, respectively, but I guess this should be allowed.