You can use any method you like, including any other package manager, vim's built-in packages or manual clone of the repo. The reason we suggested vundle historically is that it (at the time) was the only one that correctly handled submodules.

I'll write up some instructions on using the built-in packages later.

How to use vim's built-in plugins:

1. Clone the plugin as an optional package

git clone --recurse-submodules https://github.com/ycm-core/YouCompleteMe.git ~/.vim/pack/YouCompleteMe/opt/YouCompleteMe

2. Build the extension (per README.md instructions)

pushd ~/.vim/pack/YouCompleteMe/opt/YouCompleteMe
./install.py --all
popd

3. Add the following line to your vimrc:

packadd YouCompleteMe

To Update:

1. Pull latest, update submodules, and rebuild

pushd ~/.vim/pack/YouCompleteMe/opt/YouCompleteMe
git pull
git submodule update --init --recursive
./install.py --all
popd

Alternatively you can use any other package manager.

Btw, vundle is back: https://github.com/VundleVim.