White Dwarf (along with Wizard's/TSR's Dragon magazine) during their earlier years, did actualy focus on other games outside their respective domains, since they were originaly gaming magazines, and not specific game magazines.
For instance, our local Blood Bowl league commish showed me an old issue of WD he thought I would be interested in. Sure, it had Warhammer and other GW related articles in there (including some house rules for Blood Bowl 2nd Ed), but he wanted me to read it for the old Paranoia adventure published in that issue as well. I introduced the new Paranoia edition to the group about a month earlier, and he thought it might be a good idea to convert that adventure to the newest ruleset.
But yes, today, White Dwarf and Dragon are just heavily focused on their parent company's flagship games, but since the game industry wasn't in the shape that it is today, it promoted gaming in general rather than their own games.