There is a range of “take turns” dice games like this one on nRich.
I see this activity as a way of practicing key skills (in this case column addition) but in a much deeper way than repeated practice as you are working backwards to achieve a result. I would think of this as adding a significant degree of difficulty over simply doing a page of sums; it would be something you would only chose to do once the basic process of column addition is reasonably secure. However, because it is engaging (i.e. competitive) students are more likely to stick with it.
To avoid the need to provide students with 10-dice an interactive dice could be displayed on the board. nRich have this handy spinners tool here and there are lots of other options online.
All students would then have the same set of numbers and it would be a competition to get closest to 1000. You might need to note down the numbers as you go to prevent cheating!
Again, of course, the value in the activity comes from the discussion, both in pairs and in whole class. I like the idea of saying that the target is 1000 but actually rewarding good discussion and reasoning rather than just closest answer (i.e 5 points for a new “noticing”, 5 points for the closest answer)
Another way is to determine all the required random numbers at the outset and the students can fill in the grid with full knowledge of their options. Less luck involved and so probably less fun!
I would do one game whole-class, where students are playing individually. Then a second game where students are to work together in pairs competing against another pair so they can compare strategies once they have a degree of familiarilty with the problem and get some good discussion going on strategy.