The maps data is stored in
/sdcard/MapsWithMe/. For each downloaded map, there are 2/3 files (depending with route or not) and 1 folder:
<Country> folder (empty)
Country.mwm for map data
Country.mwm.routing for its routing (direction) data
You need to download the map data from your PC (using Android emulator*, refer to this question.), transfer the data from the emulator to your PC, then transfer the data again from your PC to your physical device.
* for Android emulator, I recommend BlueStacks since it's simple enough for general end-users. You can refer to this question to transfer between BlueStacks and PC.
Disclaimer: I don't have any affiliations to BlueStacks. I just tried it and found that it's easier to use than Android SDK emulator and using ADB to pull the files