This is how you can save the list of recent files from vim to a file:
vim -c "call append(0, v:oldfiles)" -c "write vim-oldfiles.tmp" -c exit
Put v:oldfiles (the list of recent files saved in ~/.viminfo) into the first (new and empty at the start) buffer, write the buffer to a file, exit.
Now you can pass the content of file to fzf.
wow, great. This is what I really looked for. Thank you very much.
and, I figured out there is no way to output the result on terminal not opening the vim. I will do as you wrote.