Now I remember, to be exact, my idea was not really about variable grouping in the combo box "move and..." but about variable sorting on main page, then you would use only "move and go to next game" in game page and it would be enough.

I think fencer noticed some of my ideas before and may be moved something to his TODO list, though more reactions from other people were only about my complex tournament rules generator idea or something I think.
"move and" would have more useful variations, for example move and close game window, move to next game of this type or wait here if none is available (with some "try again" button available) and similar, to prevent unnecessary loading of main page and so on.