Solution: A game of avoiding the neighbours

The insight needed for speedy solving is to realise that each central number links directly with six others, and thus cannot be other than 1 or 8. For example, if 3 were to be centrally placed, it would be barred from linking with both 2 and 4, despite already linking by definition with six others. This would require the diagram to have nine numbers rather than eight.

Back to puzzle: a game of avoiding the neighbours.