This is a pretty common issue on older Wiis with dual layer disc games. Not many Wii games use dual layer discs but Super Smash Bros. Brawl does, so it’s likely that your other games you’ve tested aren’t, and that’s why they work but this one doesn’t.
Here’s a list of Wii games that use a dual layer disc. If you own any of these games you could try testing them as well.
This issue does mean your DVD drive/laser will need to be either cleaned or replaced. If you’re feeling up for it, you could follow this guide to remove the laser, and clean it with a method like this (see step 3). Otherwise, if the cleaning doesn’t work, the laser will need to be replaced completely using the aforementioned guide and a new laser. However, the easier method would be to replace the entire drive.