Even if you were able to push the code to github with git lfs, it won't deploy to github pages if the file size was more than 100mb by default. As shown in your screenshot, I would advise the large files are hosted somewhere else and link those .mp4 files with some urls.
However, you can exclude the large files in your gh-pages branch by following the steps below :
Build your files with :
npm run build
Checkout to your gh-pages branch with:
git checkout gh-pages
Remove all the tracked files, including the files tracked by git lfs with:
git rm -r *
This removes all the files recursively.
Copy the files from the build folder, often dist with:
cp -r dist/* .
This copies all in the dist folder into . which is the current context of the gh-pages branch.
Then proceed to add the new changes to the branch and push to the desired github repository.
git add .
git commit -m "commit message"
git push origin gh-pages