This architecture is based upon a simple current steering dac. Although, usually it allows for differential input signal control words (\$d_{1}\$,\$d_{1N}\$,\$d_{2}\$,\$d_{2N}\$,...\$d_{k}\$,\$d_{kN}\$) and a differential load (\$R_{L}\$ on each leg).
"I dont know how exactly this circuits works. I dont understand how that feedback loop sets up an accurate know current source biasing, and what transistor is it trying to bias, Q4? For what?"
An ideal current steering dac will have perfect current sources that add (across a resistive load) to create a voltage output proportional to switches turned on or off. So you would like close to ideal current mirroring under all conditions. The current source on the left mirror leg provides feedback and a high impedance cascode to help acheive this. It can usually be set by some Rref and vref that will fix the current of the mirror source and provide robustness against variations. The loads of the mirror are each of the current steering blocks. Forcing one to be fixed with vbias will help create ideal loads for the mirror and improve matching (rather than have the loads vary with differential inputs).
The switches \$d_{1}\$,\$d_{2}\$, to \$d_{k}\$ will simply steer current proportional to the input codes and sum across the output \$R_L\$=50 \$ohm\$. So for example, if you had \$d_{1}\$,\$d_{0}\$ = 1,0 you would get half \$I_{1}\$ plus a full \$I_{0}\$ or \$Vout= \$(\$I_{1}*\frac{1}{2} + I_{0}\$*1)\$*50ohm\$.
You might have an easier time starting with understanding a basic fully differential current steering dac.
edit* per request in comment, here is a good tutorial from Behzad Razavi. Note he doesn't show much in the way of current mirror architectures, but you can look up robust current mirror design for that.
edit2* I built an lstpice simulation to help you further. It uses binary weighted current cells and nmos inputs. It should be fairly simple to translate to thermometer (X1 for each current cell weight). You can just flip upsidown and use PMOS to match book.
