Since "Modlist backup" only includes a list of the installed Nexus mods, this often includes only a sub-set of all mods. In addition it lists installed mods across all Vortex-managed games, there's no way to get only a single game (unless you only mod a single game).
To get a list of all installed mods for a single game, open-up command-line (cmd) in Windows, change (cd) to the "Mod staging folder" (Vortex mods tab, click "Open..." "Open Mod Staging Folder" gives the location).
dir /b > list_of_mods.txt
and all installed mods will be listed in "list_of_mods.txt" and you can example use Notepad to look on this file.
Note, this includes all installed mods, where's no way to get a list of only the active mods for current profile (unless all installed mods are active).
Also note, list_of_mods.txt will include a few extra lines that isn't mods, this includes list_of_mods.txt, __vortex_staging_folder and one or more vortex.deployment.*