/run/uuidd/request is hardcoded in libuuid from util-linux and uuidd
listens on this socket to provide random and time-based UUIDs in a
secure manner (man 8 uuidd). Some applications (eg, python's uuid)
prefer to use this socket, falling back to getrandom(), /dev/urandom,
etc. Eg:

$ strace -f aa-exec -p test -- \
  python3 -c 'import uuid ; print("%s\n" % str(uuid.uuid1()))'
...
socket(AF_INET, SOCK_DGRAM, IPPROTO_IP) = -1 EACCES (Permission denied)
getrandom("\x8e\x89\xa5\xe7\x39\x1b", 6, GRND_NONBLOCK) = 6
...

uuidd itself produces random numbers using getrandom() and
/dev/{,u}random (falling back to time-based if not), which are already
allowed in the base abstraction. The uuidd daemon, when available, runs
unprivileged under a dedicated user, so allowing read-only access to
/run/uuidd/request is reasonable.