Now let all this nonsense be put straight.
The direction of prayer is not a minor problem for muslims, and they have to observe the qibla (the direction of Mecca; Muhammad called his followers "the people of the qibla and the community").
The exact aim is not the Ka'ba, but the place between the mîzâb = water spout and the Western corner of the Ka'ba. So naturally praying muslims would face one another if the building weren't between them.
Nowadays the qibla shouldn't be a mathematical problem any more since we have shperic trigonometry. The faithful shouldn't draw lines on a flat map, but ask an experienced geographer.
Normally one side of a mosque faces the qibla, and a niche (mihrab) shows the direction. In Germany mosques which often are houses bought by muslims and don't face Mecca the mihrab is inserted assymetrically.
In Indonesia where early mosques have been built in a wrong direction they neglect the mihrab and use lines or threads to show the correct direction. In prayer they face North-West.

There is no cause for wondering, only the question is wrong. It mustn't be "facing East to Mecca", but "facing Mecca". E.g., in Persia you can only face East or Mecca.