It's not difficult to fix. Well, it is a pain in the ass, but you can do it, for low dollars. Step 1 is to buy a sample size piece of that 3m paint film. Wrap it around the handlebar, under the grip. Make it the perfect size, and that play is eliminated. This lasts forever as it's designed to stand up to abrasion. I've done this for years, on all of my bikes.
The side to side is not tough, either. You need superglue and a package of something that was wrapped in plastic. I used some teflon I had laying around, from another project. Clear plastic works well, too. It has to be thin. Something thin and flat, like a 9volt battery package. That sort of plastic.
Use one of those hole punch machines. Use it to punch holes in the material and save the round piece. You then superglue that to the throttle tubes sides. Make these bearings oversize, and sand them down until the fit is perfect. I think I used 4 in each side of the tube. Avoid placing them where the cross the seam in the throttle housing. You can only see 2 in the picture. The others are hidden by the housing.
This should last for the life of the bike. It's also a really good way to cut down on vibration. Just doing this to the throttle does not accomplish much, but when you do stuff like this to all the controls, the bike feels better.