Given the (necessary) structure of CHYOA, I'm rather against it. Having to type both names for each score change is a lot of extra work. (though it would be possible to change the display name each chapter) Having the predefined variables is not quite easy to use and you would always need the help of the story owner to introduce new variables for your branch.
Is it possible that game variables are still defined inside chapters but there is a list of them like immersion variables so that they can be copied.
Hm... I guess they could be collected story-wide like tags, so it should be technically possible. A list seems to be unpractical. Maybe a dropdown menu and if you choose a variable, it is inserted at the cursor position, no matter what field you are in. (Though I'm not sure if the cursor position stays the same as soon as you open the dropdown menu.) Another possibility might be to type away and choose but that might not work for the chapter text.
If you are talking about drop down menu, immersion variables should have a drop down menu as well. Maybe there could be two drop down menus at the side (where immersion variable's list is placed right now). The number of immersion variable in a story can also be a lot so a list is not practical for them either. Maybe put the drop down menu at side but just for copying from it instead of inserting at cursor position if cursor position is changing or any other problem is arriving. There is a list for immersion variables right now and probably most people just use it to copy from it like me. But if you use drop down menu and it puts the text in cursor's position it might be an improvement. If it does not work just make a drop down menu so that writers can copy from it.