Cubulous

Cubulous is a 1987 game by Benedict Einstein, and was self-published.

Cubulous is a board game using dice as pieces, and not as random generators. The top face of the die determines its moving range. And the dice move to the next square by flipping to their next face.

The game is played on a 9x9 board, with eight dice per player, plus two shields and one master:

the game's material (not the setup, check rules below) 

Here are the official rules: 

Duell

Duell, aka Conquest, is a 1975 game by Geoffrey Hayes, published by Alga (among others).

The game is played on an 8x9 board. It uses dice, not as random generators, but as pieces. Each army has eight regular dice, plus a 'key piece' with one dotted star on every side.

The setup is as follows (with all faces 4 facing inwards):

The rules:

• Regular dice move by 'tumbling' their faces over the next empty square (there's no diagonal moves; there's no jump over other pieces).
• The initial move must be forward or backward
• Pieces can also turn right or left during the move; this can be done just once during the move
  
• The number of moves is given by the die's top face; the piece cannot stop until the entire move sequence is done
• Key pieces can only move one square per turn (after all, all their faces have a one)
• Capture is by replacement and is only possible at the last square of the moving piece
  
• Wins the player that captures the enemy key piece; or moves his own key piece to the initial square of the enemy key piece (so White's moving from e1 to e8, or Black's from e8 to e1).
  

move examples from the rule book

Some hints given by the rule book:

• It is sometimes possible to approach one square from two different paths.
• Your choice of path will determine what number will be on the "top face" of your piece at the conclusion of the move.
• Your strategy can include planning for a subsequent move if you can control the top number and space location.

Here's a review from GAMES magazine #2: 

From Science & Vie #736 (1979): 

And from Games & Puzzles #48:

There are not that many abstract games using dice as pieces. We already mentioned Chase (1985) here in the blog. Other examples are Mojave (2004) and Cublino (2006).

Chase

Chase was designed by Tom Kruszewski in 1985 and published by TSR.

Clark D. Rodeffer and me (João Neto) wrote an article about it in Abstract Games Magazine #9 (2002). It is a remarkable game that, sadly, is almost forgotten. I recommend reading the article and try yourself the game.

Some words from Steffan O'Sullivan in 1997:

Bumps and exchanges are other key elements to watch out for in the game.You can carefully set up a fork, thinking you've got a good capture going next turn, when suddenly he makes a bump move which protects both pieces at once and threatens a move to the Chamber!

One thing chess players have a hard time adjusting to is the concept of exchanges in this game. It seems like a good exchange, trading a "1" die to capture a "6" die, but after the exchange, you both have the same number of dice totalling 25! Very puzzling - you have to learn to think differently than in chess.

As your dice pool dwindles, you become less flexible. Yes, you still have 25 movement points total, but if those are concentrated on five dice as opposed to spread out over nine dice, you'll find it's harder to make all kinds of moves. Most dice will have high numbers, and you can't creep up on the enemy. Even worse, you can't afford another loss at that point, and the game gets very tense. Most of the strategy centers around the Chamber: he who has the most dice at any given moment is ahead, unless his position is really lousy.

Position is something that takes time to learn: there are key rows which radiate out from the Chamber that are very important. It's also important to keep at least some of your dice together. Not only does this allow for Exchange moves, it also makes for some good bumping. But this is something you'll learn best from playing the game, so I won't go into detail.

Chase can be played on AiAi.

Here's another review from Sid Sackson in GAMES #68,