Public transport in Iceland is infrequent. There are no trains in Iceland and very few options for traveling between places by bus, and they are not a good fit for the chess tournament in Skjólbrekka. Buses from Keflavík Airport to Reykjavík are a good option, as there are many of them every day. However, if you are going outside Reykjavík and to other places in the countryside, there is usually only one trip per day available.
Unfortunately, there is only one bus trip per day between Reykjavík and Akureyri and back. On weekdays, the bus leaves Reykjavík at 14:48 and arrives in Akureyri at 21:23, so that timing is not suitable unless you arrive the day earlier (Wednesday 18 November).
The same story can be said for the Akureyri – Reykjavík trip on Sunday 22 November. The bus leaves at 14:03 from Akureyri (Hof) but the last round of the tournament starts at 10:00 so it is unlikely that players will be able to make that trip, as it is a 60 minute drive from Skjólbrekka to Akureyri.
The next day, Monday 23 November, the bus from Akureyri to Reykjavík leaves at almost the same time 13:49 from Hof. Arrival in Reykjavík is scheduled for 20:25 (Mjódd).
So taking a bus from Reykjavík to Akureyri and then somehow getting to Skjólbrekka is unlikely unless you have enough time and can stay one extra night before the tournament and one extra night after the tournament ends.
There are many daily bus trips from Keflavík Airport to Reykjavík (route 55) and then take route 57 from Reykjavík to Akureyri. Here you can see what time they are. Keflavík airport – Reykjavík by Bus.

Seyðisfjörður (By the ferry Norræna) to Egilsstaðir-Skjólbrekka

