The date is from 2002. I'm a nursing student. Some of these REM concepts he's talking about are somewhat false. I would not advise that this method of sleeping is helpful.
Depending how sleep deprived you currently are, REM takes 30~90 minutes to activate after stages N1, N2, N3 and N4 of sleep (or the NREM sleep). If you're updated with the current trends, N3 and N4 are combined as N3. After a completion of sleep, it repeats itself to the NREM stage and goes back to REM. If you're doing this, you'll actually miss your REM sleep since a 30 minute nap can make you miss your REM stage.
If you're planning to sleep deprive yourself, you'll quickly finish your NREM to enter REM sleep. Although REM sleep is the signal of a complete cycle of sleep, the NREM part (specifically N3 and N4) of sleeping helps build your body, recycles your fluid, and repair tissues. Sleep deprevation will also increase your chances of getting an infection immune system's function is weaken or impaired and you're more prone to judgmental mistakes. REM sleep will be faster to enter, but there isn't a huge significance gain compared to NREM. However, theories speculate that REM can improve your memory as well as feel stimulate due to the introduction of monoamine transmitters. Link
These monoanimes are anti-depressants.
tl;dr - In other words, you'll feel
If you want my advice, just find a day or a weekend and see how long can you sleep. Set an alarm and measure how much of sleep do you really need and when your REM sleep occurs and use that as your guide. Everyone needs a different amount of sleep, but everyone needs sleep.