I'm going to be a bit contrarian and say that it may be more beneficial than the other answers here seem to imply. The reasoning is simple - what is the easiest way to remember a series of moves? Not by simply remembering which piece moved where, but by understanding what the purpose of each move is.
And if you know the purpose of each move, your mind may start to associate the remembered patterns with the purposes. This seems to me that it could be quite beneficial.
Now I'm not saying this is better than other forms of training, but if you particularly enjoy this activity, then it may be more productive than doing another form of training which you don't. Personally, I can't imagine why anyone would enjoy remembering details like this, but to each his own.
In addition, given a historical chess position, many GM's can easily recall which game the position is from (I saw a documentary where Carlsen was given a position from a random historical game and he got most of the information about the game right; he remembered who the players were, but I think he got the exact year slightly wrong). This indicates to me that GM's spend a non-trivial amount of time studying and remembering other games - it would be strange to dismiss this form of training out of hand.