The OP's picture is a half-complete instrument. The tangents (the vertical metal pieces that press the strings) and the strings themselves are not yet in place, so it's hard for a "non-expert" to understand how the finished instrument will "work".
The pictures in the Wikipedia link are of complete instruments, but the back of the keys is partly covered by the felt dampers which stop the "unused" part of the strings from vibrating.
The tangents will be at the end of the dog-leg part of the keys, i.e. in a diagonal straight line running across the instrument. The "working length" of the key levers is thus shorter in the bass than in the treble, which applies more force to the bass strings for a constant finger-pressure across the whole keyboard.
The strings run in a parallel band at an angle to that line, with the bass strings at the front and the treble strings furthest form the player.
The geometry of where the strings must be "touched" depends on the shape of the curved bridge (on the soundboard at the right) and where the left hand end of the strings are fixed. The bass strings extend to the left hand side of the instrument but you can see the pins for the treble strings along the back of the case. (The positions of the tuning pegs for the strings, on the right hand side of the soundboard, have been marked out, but the pegs are not yet fitted). Any intentional variation in string tension between bass and treble, also affects the geometrical layout.
The second part of the dog-leg "behind" where the tangents will be, is just a matter of fitting the keys into the case. The back of each key is slides up and down on a metal pin fixed into the back rail of the case, to stop the keys wobbling sideways. Therefore the back of the keys need to be wide enough to contain the slots for the pins without the risk of the wood cracking, and more or less evenly spaced along the back of the instrument.
All these geometrical compromises apply to both fretted and unfretted clavichords. The main difference in design is that fretted instruments have fewer strings (since two notes share the same string and can not be played together) which reduces the "depth" of the instrument from front to back.
Incidentally, keyboard-making was considered to be the most skilful woodworking task in building these early keyboard instruments. To avoid problems caused by the wood warping, the traditional way was to cut the entire set of keys out of one solid plank of wood, so that after cutting (using nothing but hand tools, of course) any changes in temperature and humidity would warp them all in the same direction, and minimize any problems with adjacent keys jamming against each other. Make one mistake, and the whole keyboard was firewood!