I'm not familiar with the original Mighty Empires game. However, in the last six months, a friend purchased the "new" Warhammer: Mighty Empires tiles, thinking that they might be fun to use in relation to a campaign for Lord Of The Rings: Strategy Battle Game. I think they would be fun for that purpose as well. But what might also be fun is to use them in relation to a traditional "sandbox" OD&D campaign.
My thinking is this. The DM places the first tile, likely with the town or dungeon that the characters are starting on. Then, as the characters explore outward, you add more tiles to the original starting tile, "revealing" the map as you go. This might be particularly enjoyable if doing so eventually leads to the D&D endgame: one of the characters selects a tile on which to establish their own stronghold, and continues to expand outwards from that tile, taking control of more land, populations, and resources as she does so.