Does this game or the other have a playing-as-Grendel element, a la the Beowulf remake novel, Grendel?

This game is not quite what you think it might be.  In fact, other than the artwork, the Beowulf license doesn't really apply to this game at all.

This game is an updated remake of Reiner Knizia's Kingdoms.  It is mostly an abstract tile-laying game.  On your turn, you either lay down a tile (usually with a number between -6 to 6, though some have special abilities) or a scoring piece with a value of 1 through 4.  The pieces are placed on a grid.  At the end of the round, you add up the tiles in the row and column that your scoring piece is in.  You then multiply that value by the value of your scoring piece.  The total value of your scoring pieces over three rounds (each round played on a different sized grid, and with different sets of tiles) is your final score.  Player with the highest wins.

It combines strategy and luck.  The tiles are drawn at random, though you keep a hand of 2 at all times.  But it is deciding when and where to place a tile as well as when to place a scoring piece and which one in order to maximize your score (the 2-4 value scoring pieces are one time use, the 1 value pieces are are returned to you after each round).

It is a fun game when played with other like-minded players, but it in no way evokes any sense of the move, nor is there really any opposite POV to deal with.

Agreed.  Grendel doesn't even enter into it.