Hold the pedal all the way to the floor and don't let off. Mine gets up to almost 7k before it shifts. It needs to be in probably 1st or 2nd to really hold it all the way like that. Starting from a full stop and just mashing it should work. Once it's in 3rd it really doesn't have enough tq to hold to redline anymore and these cars try to shift as quickly as possible on you. Mine drops to 3rd at 18-19mph if I'm accelerating normally/slow. If you're rolling out from a toll booth doing 15mph the car is most likely already downshifted on you so far that you won't be able to redline it.
That's also a terrible video. He says "yeah feel the vtec" at around 1:10-1:15. Dude has no idea how his car works. He should really be saying "yeah, feel the vtec stop!" He's just coming to a stop and flooring it. 1st gear pulls to redline. 115hp/128tq. Whee?
If you have an auto, putting it in 3, 2, or 1 will lock the transmission out of any higher gear. If you put the car in 3 instead of D it will limit you to 1st, 2nd, and 3rd gear. Effectively you can then reach redline without the car shifting to a higher gear. I don't know about your particular year but if i put my car in 2 it stays in 2 and doesn't use 1st to get going. Starts are definitely a bit slower but you can hold that gear pretty much up to about 60mph.
Try driving around on some roads where the limit is 40-45 and put the car in "3" for a day and see how you like it. I do that at the Dragon and other spirited driving sessions. It will heat up your transmission a lot though holding higher RPMS. Very fun and you can use the little bit of power you have a lot easier. "2" is really a blast but the RPMS will be way up there and it's kinda noisy. try that also. I think you'll like it.
Do this if you want to run around in 2/3:
http://9thcivic.com/forum/threads/diy-at-transmission-cooler-dx-lx-ex-not-for-cvt.13700/