@bh123 I just finished writing a long explanation but an errant finger swipe wiped it out. (I hate that when it happens.) Let offer my non-expert interpretation of the numbers. The tube spec of 60 mA describes the current that should be found at the cathode of each 300B after the amplifier is well warmed up, but not playing music, it is the ‘idle current.’ When Atmasphere builds his amps, he designs his circuits to be capable of delivering 60 mA to the cathode of each 300B in order to bias it for proper operation. You can thinking of it as adjusting the trigger pull of a gun. The tube needs the proper bias current in order to be ‘ready to go’ whenever it senses the incoming signal.
Conditions can vary at the cathode, tubes have a break-in period, and during this time the bias current must be closely monitored. The cathode slowly erodes from electrons flying off the cathode to the plate all the time the tube is in use, so the current to the cathode needs to be adjusted occasionally (every month or two) in order to keep the amp working in top form. Many manufacturers offer individual potentiometers at each tube, with switches and a meter so that the user can check and adjust the bias current at any time. Your manufacturer has included an auto bias circuit, so you don’t have to check such things, the circuit takes care of it for you. The correct bias current for a 300B tube, regardless of who manufactured it is given in the ‘Static Parameters’ you list: it is 60 mA as specified.
Once the tube is operating, music or test signals passing through, the current will begin to vary in response to (1) volume knob or magnitude of the input signal, the frequency of the signal which may trigger, (3) different impedance, or AC resistance, at the load. The current must not get too high or the tube is damaged. This is where the ‘Maximum Ratings’ you list above the Static Parameters come in. Your tube should never exceed 100 mA of ‘Ki’or Kathode current if is is in a circuit employing Cathode bias, as yours does (and never more than 70 mA if the circuit is designed with fixed bias).
Due to the nature of tube manufacture, age of the tube, etc. there may be slight differences in the way to different tubes perform. The best way to grade tubes and provide a means for ‘matching’ pairs or quads, is to test them. A speaker is replaced with a dummy load, a constant frequency signal (often 1000 Hz) is input, ‘volume’ is set to a specified voltage range (voltage output as viewed on an oscilloscope), and the tube is warmed up and tested for the current at the cathode. Under test conditions, your tube measured 80 mA, that is why ‘80 mA’ is marked on the tube. It could then be matched with other tubes which also tested out to 80 mA and thus pairs and quads could be formed with some assurance that they would perform is a ‘balanced’ fashion upon installation.
I hope this is enough information to ease your anxiety. Remember, I’m no expert. I think I know how you feel. I’ve been there, I expect we all have been at one time or another. Your system and your tube is fine. If the tube starts glowing red or white hot, shut it down, if you hear popping sounds, or smoke starts rolling out from under the chassis, pull the plug pronto, otherwise sit back and enjoy the music.
Edit: The manufacturer may specify a different bias for the tube in his or her design than that specified by the tube manufacturer; follow the manufacturer’s recommendations (this is not a concern for you, @bh123 ).