The game is most likely Hnefatafl, the ancestor of a family of derivative modern games referred to as tafl games. Hnefatafl was the most popular board game in early-Medieval Europe, having accompanied the Vikings (who invented it) around Europe during their conquests and raids, until displaced by chess later in the era.
I was able to find Whittaker, H. (2006). Game-boards and gaming-pieces in funerary contexts in the Northern European iron age. online, one of the citations in the original article. It discusses (in English) the context, analysis, and conclusions derived from the frequent association of board game pieces and equipment with high status, usually male, individuals from iron age Nordic burial sites.
The game-boards and gaming-pieces found in northern European graves of this period are usually considered to have been used for playing Hnefatafl, a game which is well known from textual evidence. Hnefatafl was clearly a game of war, and it would seem not unlikely that playing the game was regarded as useful to the development of warrior abilities.
The older citation from van Hamel (1934) appears to not be available in English.
Although no description of the board or of the pieces has yet been obtained in answer to this question note the following:
Numerous tafl variants, on various board sizes and with different numbers of men for both sides, have been described in the Nordic Sagas and discovered in Viking graves.
The tafl variant most commonly mentioned in saga literature, and most commonly found in Scandinavian graves, seems to have been Hnefatafl itself; as noted above by Whittaker.
Hnefatafl is an asymmetric game, with a designated attacker and defender of unequal strength. One of the defender's pieces is a King, and the object of the game is, respectively, to capture the King (attacker) or rescue the King (defender). Typically the Attacker would have about twice as many pieces as the Defender, not counting the King.
The old 1960's era game Goldfinger, by Milton Bradley, is similar and would impart some of the flavour for this style of game, for those old enough to remember. Certainly my brother and I spent many enjoyable hours playing this game in our pre-teens.
Goldfinger is hiding in Fort Knox (the center of a 9X9 grid) guarded
by 8 henchmen (blue). 16 agents (red), under the guidance of Mr. Bond,
have been sent to apprehend him.
Movement of pieces is easy... move any one of your men any distance
along a straight line. If you can trap an opponent's piece between two
of yours, it is captured and removed from the board. Goldfinger
requires all four adjacent points occupied before he is captured.
The object for the red player is to capture Goldfinger; for blue to
win, Goldfinger must escape.