Is this a H-Bridge, why are the two ICs there?
Is this a H-Bridge, why are the two ICs there

Each IC is a half-bridge driver: -

And, two half-bridge drivers control 4 MOSFETs in a full H-bridge

Is it because you can't use the MOSFETs with as low voltage as 3.3V ?

The MOSFET gates probably need significantly greater than 3.3 volts to turn on the device properly hence, the power rail for the chips is +10 volts. In fact, page 4 (figure 3) tells you that you should really be using in excess of 6 volts of gate voltage to drive the IRFH7085PbF properly. This is to avoid thermal runaway and device failure.

Can't the IC just assume, if there is no high on the HI pin, there is
a high signal on LI ?

No you can't; the two chips have to be connected with inverted input signals as per the red and blue boxes in the picture below: -


Can you tell me something of the overall &quot;quality&quot; of this circuit ?

Well, the motor is not stated so we can't tell what sort of load current it will pull so this stops us in our tracks from any reasonable analysis. Neither are there details of the power supply so this doesn't help either.