Not sure of your help page referenced but maybe my explanation below will help. Since they reference 960 I'm guessing that was written a while back before RB/BiaB got higher resolutions.
When MIDI sequencers started being popular, 120 resolution was standard for many, if not all of them early on.
As for computer CPU load, any affect would be so minute as to be imperceptible in 99%+ of cases.
You'd be surprised how much of the time an AVG CPU is waiting for something to do. It is rarely the bottleneck. A 'sign' that the system is struggling is usually the cursor not moving smoothly during playback. Whenever I see this, I save, close out and reopen. This lets me know I have burned this session, but that's a whole 'nother aspect of DAW use (resources).
Lets start with audio and resolution. Doing audio edits is downright painful at 120 resolution. It is dang near impossible to get a clean cut/paste of a waveform exactly where you want it. The image below is zoomed in to show where a bass note begins on a track (it starts ahead of the beat as you can see). Anyone who has done audio editing knows you want a clean edit to avoid the nasty tell-tale pops/clicks of poor editing jobs. If I want to start this edit exactly where the bass note starts (sometimes called the zero point) I can do it very exacting using 3659 (with resolution at 3840).
With resolution at 120 I would have to decide on whether to use 114, which has the tail end of the previous note included, or 115 which is even worse because it is well off the zero point and will almost certainly make a noticeable click.
Then I would have to fight the same battle when deciding where to paste it in.
Does this make sense? I think this is why some think audio editing is terrible in RB; if you are trying it at 120 resolution it will be very 'clunky' and 'chunky'.
Now let's talk about MIDI and how Tempo and Resolution combine.
Since Resolution is defining the number of slices per beat, the number of beats per minute determine just how small a chunk of time each slice is.
At tempo 120 each beat is 500 mS (half a second).
If resolution is also 120 then each 'slice' = 4.17 milliseconds
If resolution is set to 3840 then each slice = 0.13 milliseconds
At tempo of 96 the results are 5.2 mS compared to 0.16 mS. Still huge difference.
Now if your most precise 'slice' of digital information is going to be every 4 to 5 milliseconds or so, every piece of data that comes in to get recorded (think MIDI here) is going to be written in one of those chunks, whether you played that note at exactly that point in time or not.
As an example Year of the Cat by Al Stewart comes to mind. Listen to the opening piano.
https://www.youtube.com/watch?v=zvBfIdhG974 If this were recorded (in MIDI) at 120 resolution some of the nuance of this performance would be lost. If the Cmaj7 chord and D6 chords did not roll (arpeggiate) the way they do the song would lose some character. Instead of each note being adjusted a tenth of a mS or so (at 3840), each note would be adjusted 5 mS or so at 120. The larger the chunks of adjustment the less 'real' the performance is. It's important to understand that no matter what actual point in real-time a given note was played, it is going to be written to the nearest 'slice' available.
Many times it may not be perceptible, but sometimes it is. If just 2 of the notes in the above referenced chords ended up being written in the same time slice, it changes what was actually played. In essence it has been quantized.
It is very small, but quantizing is actually taking place and you can decide how you want your performance quantized from the very beginning.
Once recorded at 120 resolution though, going to 3840 later does absolutely no good for MIDI. However, it does for Audio! you can raise your setting later to get more surgical control over edits.
What's interesting is RB/PT use MIDI to control audio events. Audio snips are 'triggered' using MIDI. To understand this open the Event Editor for an audio track.
The bottom picture shows a typical audio track here that has had edits done. Notice the resolution is at the 3840 setting .. makes for more accurate edits as mentioned above.
Hope this Helps explain how I look at it.