OK, I've done a bit of research so that this topic isn't completely
sidetracked...
Trying to strip down Lakka to meet the FSDG doesn't appear to be an option.
As I read it, http://www.lakka.tv/get/linux/generic/install/first-boot/games/
seems to suggest the whole point of the distro is to run ROMs of other
console's games: quite contrary to the aims of libre distro. That said, it is
still worth looking at Lakka to consider what GOLD could learn from it.
In regards to software management/updates, I would suggest apt or something
similar, with a three-way division of the repositories between system core,
fully-free games, and non-free art games. Something like GNOME software could
be thrown in for a games store, only showing the games repositories; system
updates could then be delivered via an auto-updater, which would maintain the
system core.
By dividing the games into two classes, like above, the user is provided with
choice in regards to whether or not they wish to allow non-free artworks
(although whether this is desired is obviously up for debate). The choice of
apt, or similar package manager, is based on what level of control is
desired. Lakka (and its base OpenELEC) seem to use a much more basic package
management system, which assists them in shedding weight; however, it seems
that fine-grained control would be of more interest in a free-software system
than absolute minimalism.