Yes, I do now understand the importance of boots for Rengar. I've been getting in more and more situations where I need boots and have been forced to build them and my chases and escapes have been improved greatly. I'll be updating this build soon. Thanks for the criticism and if there is something else about the build that I could improve on please let me know :)

The one thing better than mobility, is more mobility.
There's a reason a lot of rengar players run Mobility Boots + Flash + Youmuu's Ghostblade - it's because rengar's mobility is so strong, that it'd be foolish not to take advantage of it

^
If you don't understand this, you don't understand the game. Pure and simple.

The fundamental flaw with your entire logic here ignores the fact that in zero lanes are there and stretches of grass where you could ward and leap over a wall as Rengar. And assuming your ult is on CD to just it to leap to a monster to get away, means you are forced to basically be feed, unless you can bola kite. Which is a lot harder than you think, because you have to stop to fire, and at max range have a good chance of missing. Another rather large flaw is that you assume all battles are going to take place in the river or jungle, where there is plenty of grass for you to run through for the speed boost from the necklace, which any one who plays LCS, or has watched the WCS, knows that a better part of the battles take place in the lane, where you're wide open, and in a lot more circumstances away from any grass you can make a leap from.

I personally tried your build out, and on paper yeah it looks great, but I lose a MASSIVE amount of move speed while in stealth because there's no boots of speed or Mobility with either Furor, or Alacrity enchants, which allows for a chase and gap close, or a juke escape from the enemy team if you're found alone, or just low on health and don't want to be a free kill. The move speed difference with your build, three stacks on Necklace, and with Trinityforce, was 405 TF/BTN, and something like 475 BoM+Alarcrity/BTN. As you can see, that is a HUGE speed boost difference, and with max stacks of BTN, speed caps out at 950, without having to use YG, or BotRK.

Secondly your guide for the Q spam is actually horrible. Most played champs have some sort of CC or peal to get away after the first Q, and champions like Katarina, Master Yi, Ahri, Tristana, and Corki, to name a few have incredible peel/escape.

Instead you should open with a full fury Bola to net them, use Battle Roar to get yourself some survivability and chase with a Savagery before your Fury refills. Depending on if you were only in stealth for a few seconds, not enough to get full fury, use a bola for the slow, after the snare breaks, then snare again. This way you can single out a target trying to give chase, or if you were in stealth for five seconds, split a team while you give chase. Either way you take someone out of the fight.

To be completely honest, the ONLY way your guide could become useful or viable in any fashion, is to sub out the life steal quintessences, for Move speed to compensate for the loss of not having boots in this build.

Sorry but just two short term speed boosts from on use items, or heal for an even shorter speed boost, just really doesn't cut it.

Honestly, if I had to rate your guide, I would give it a -3 after trying it out, and being sorely displeased with the outcome.

If you really wanted to negate the need for boots you should sub out all of the life steal items, for Zephyr, Phantom Dancer, and Static Shiv. MAYBE, then JUST maybe could you truly compensate for the lack of boots. In short, your build and guide rely to much on specific circumstance to be effective the entire match, which is just not possible on any level.

And just so you can't really come at me, for not being a ranked player with a high ELO, here are two matches I've played. One using your guide, and one using another guide here on Mobafire.
A match using your build.
A match using a guide with boots.

yeah man you need boots and flash. if u watch worlds then you will see all rengar junglers take flash and get boots

^

Boots and flash are not necessarily needed. You need an escape over a wall, just put a ward on the other side of the wall if there is a monster camp and leap to them if you're in a nearby brush or you can use your ult to activate your passive as well. Your ult can be used to escape in other means as well. Also your leap is better than flash if you're trying to get closer to someone because it takes your right to your target instead of only a certain distance. I do understand that this limits you greatly to brush and it only has a certain range, but if you are prepared, you should be able to either drive them closer to the brush or get the brush soon enough before they are out of range. Your ult is also a better gap closer than flash because it stealths you and your target never sees you coming (granted there is no pink ward). Also if you have enough trophies you get the bonus movements speed while in stealth or using Thrill of the Hunt and then bonus movement speed from Thrill of the Hunt's passive coming out of stealth. The bonetooth necklace also makes boots unneeded because of the movement speed it gives you from brush and stealth as well as the movement speed bonus from heal. Since most of your chases should be in the jungle and there is a lot of brush in the jungle, it makes the purchase of boots obsolete. Sorry for the long explanation lol.

Flash and boots are mandatory.