How to explain the behavior of a PNP transistor as a transimpedance amplifier?
It's just a common-emitter amplifier stage. Imagine it flipped around (NPN) with just R6 as the load (D1+D2 and the transistors just have a constant voltage drop of 2*Vbe to a first approximation. 

In the actual circuit, when the base goes lower, the base current increases and the collector goes higher, so it inverts just as you'd expect of a common-emitter amplifier. DC feedback (and AC feedback) is provided for the circuit as a whole by R7 &amp; R8, so that's where the bias is coming from.

This circuit can be analyzed as three blocks- input 'long-tailed pair' Q1/Q2, Q3 which amplifies the voltage appearing across the collector load of one of the transistors, and the output voltage followers Q4/Q5. The diodes are intended to reduce crossover distortion and bias Q4/Q5 locally so they conduct a bit. The circuit would still work without the diodes D1/D2 (replaced with a short) but would produce more distortion. R2/R2 provide input bias and R7/R8 determine overall feedback. C1 and C2 are coupling capacitors. Incidentally, as Olin mentions, I've found it's usually best to think of transistors as current-operated devices when analyzing bias and switching behavior, but as voltage-operated devices when analyzing small signal behavior. In this circuit you'd want to find out where the bias is so you know that the transistors are biased properly and not saturated, but to analyze the open-loop gain, for example, you'd need to use small signal analysis.