A typical reason to have an input transformer is because the source is balanced. A guitar output is not balanced; it has a hot and ground. Balanced signals have two hot conductors that have the same impedance with respect to ground. They might also have the same signal, just 180 degrees out of phase, but they don't have to; the balanced impedance is the defining feature.
Balanced signals are useful because it makes it easier to filter noise that gets picked up between the source (microphone) and amplifier. Because both wires have the same impedance WRT ground they both pick up the same noise with the
same phase. The noise signal in both wires is going up and down at the same time WRT ground. It's called common mode signal. Meanwhile, the music signal is differential mode; it is the difference in voltage between the two wires.
So, if you have some kind of fancy electronics that can separate the common mode from the differential mode signals then you can recover the music and reject the noise. The earliest way to do that was with a transformer. Today it's cheaper to build an amplifier with balanced input by using clever electronics. Transformers are expensive. As a point of interest, old school wired telephone systems were all balanced. Think about it: thousands of miles of wire strung along the same poles that carry electricity, yet you never heard ANY 50Hz or 60Hz hum. Part of the reason is that the frequency response was deliberately band limited to reject frequencies that low, but the main reason was the balanced circuit.
Anyway, this is actually a common mode choke, not a transformer. It filters out much of the common mode noise. The rest will be eliminated by the input transformers.
This is the first input transformer. The balanced signal goes in pins 8 and 9.
The output, minus the common mode noise, is taken off of pins 3 and 4. But what about pins 5 and 6? To understand them, think in terms of current instead of voltage. The differential mode music current goes in pin 8 and comes out pin 9 - or the other way around, really back and forth because it's an AC signal. Along the way it goes in and out of pins 5 and 6 and then through the second transformer pins 3 and 5. So the same signal current goes through the primaries of two input transformers.
I admit that I don't know why they did it that way, nor do I have a good grasp of the rest of the circuit. Maybe Nuuska can shed some light.
