That microchip link. the figure 10, block diagram of a 3phase inverter bridge is just a naming convention right ? figure 9 shows the internals and table 3 and 4 shows the sequence of how it was activating in pairs to redirect the points UVW to be both power and ground via the 6 transistors/MOSFET/LGBTs (Qs). The pulses are still DC and not AC. even if it is PWMed. There was a guy in youtube that converts the AC alternators to brush-less motors that have better explanation than me. Maybe if I look up that one, would be better.
I suppose you could call any name assigned to anything a naming convention. But the term 3 phase inverter is what it truly is and what people in the industry call it. Look up the definition.
Inverter: an apparatus which converts direct current into alternating current.
And the current does alternate or change direction.
A solid state circuit to generate 3 phase AC power would be the same (although the control of frequency would be different because the BLDC circuit has to be kept in phase/synchronous with the rotor). Most of that note deals with what are often called "six step" drives because there are 6 states of commutation (switching what coils receive power similar to a brush commutator in a brush motor) as seen in 3 and 4. Note that only two windings are used at a time. For the case of figure 10 it would apply power to all 3 phases at the same time and the applied voltage (averaged because it is applied as PWM, pulse width modulated) and current will be sinusoidal just like from a power utility (except for the higher frequency PWM which is sometimes filtered out between the control and the motor, usually only on fairly high power systems).
The pulses are positive and negative so looking at any one or group of pulses you could say it is pulsed DC. But it also has pulses of the opposite polarity so most people don't consider it DC because the polarity alternates, thus it is alternating voltage and current. Doing a quick search I see some on line say it is still a DC motor although the one I saw was referring to a 6 step method of drive. Most in the industry wouldn't say that.
Often for 6 step drive the motor is designed to have trapezoidal (flat topped) back emf. This is to better match the driving voltage and reduce torque variation as the shaft rotates. A lot of more modern motors have sinusoidal back emf and are driven with sinusoidal driving voltage and power all three windings all the time.
The terms used can get confusing. For example an induction or stepper or SR motor could be called brushless because they don't have brushes but the term is not usually applied that way because it is understood that those type motors never use brushes.