This is what I tried, but it made no difference. Is there some other way for me to try?

1) in creating the AppImage, I ran the following 2 lines. The 2nd line is the usual.

export "LIBVA_DRIVERS_PATH=/usr/lib/dri:/usr/lib64/dri:/usr/lib/x86_64-linux-gnu/dri:/usr/lib/aarch64-linux-gnu/dri"

 /proj/appimage/linuxdeploy-x86_64.AppImage --appdir=AppDir -o appimage ...

That made no difference.

2) so I did the full build again, using the export line first and then ran linuxdeploy to make the appimage.

Still no difference.

The reason I know it made no difference is because instead of the path being /usr/lib/dri:..., I changed it to exporting the path to a dummy value of /etc/fstab instead and the vaapi and vdpau settings still worked.  Any suggestions?

"LIBVA_DRIVERS_PATH=/usr/lib/dri:/usr/lib64/dri:/usr/lib/x86_64-linux-gnu/dri:/usr/lib/aarch64-linux-gnu/dri"