Where does it say "all 7 channels"? When all else fails, read the manual (RTM)
www.intl.onkyo.com/downloads/manuals/pdf/tx-rz820_bas_adv_manual_en.pdf. See page 38:
■ Amplifier Section
Rated Output Power (FTC) (North American).
With 8 ohm loads, both channels driven, from 20-
20,000 Hz; rated 130 watts per channel minimum
RMS power, with no more than 0.08% total harmonic
distortion from 250 milliwatts to rated output.
Surround Mode Output Power (*)
(6 ohms, 1 kHz THD 0.9%) 200 W per channel
* Reference output for each speakers.
Depending on the source and the listening mode
settings, there may be no sound output.
It doesn't clearly say it, but the US Federal Trade Commission (FTC) specifies measuring output power when two channels are driven. Your AVR can deliver 130 watts/channel when two channels are driven. Note that the FTC numbers are measured at 8 ohms impedance, from 20-20,000 Hz (the full audio range), and at 0.08% total harmonic distortion (THD). Generally, any level of THD below 0.1% cannot be heard.
Those specs on p 38 go on to say "Surround Mode Output Power is 200 W per channel at 6 ohms impedance, measured at 1 kHz and at 0.9% THD. These conditions are much less stringent than the FTC requirements, and not surprisingly, result in a much higher power rating. Note that it avoids mention of how many channels were in use. You should ignore this.
The rest of the numbers on that page talk about amplifier power ratings for Europe, Asia, and Australia. Ignore them also.
What the rigorously measured power output is when seven channels are driven is not stated. You can be certain it will be lower than 130 wpc, but how much lower, without measuring, would only be guessing. Some independent reviews do measure the power with all channels driven, but I don't know if there is that kind of info about your AVR.
Despite all this, I wouldn't worry about it. An FTC rating of 130 wpc is hardly puny. It should be enough for most speakers and owners.