I know this build includes no boots. But the way this build works is that by mid game, even with half health, if you 1v1 and you spam every ability onto 1 opponent they should fall in less than 5-6 seconds and are slowed. Which is to little time for them or you to run away thus a player needs no boots to chase with or flee with. Of coarse with my experience this usually leads to you being the gank target (99% of all my deaths with this build minus the runes is due to enemies abandoning their lanes to gank me) but don't worry. Even with that flaw most of the time you'll kill one or two of them as they gank you (and if just two of them 50% survival chance) and this leaves the other lanes open for your team mates.

The reason this build goes all out on building the Void Ooze is for minion crushing. By the last phase of the game if your team mates can handle anything from 1v2 to 4v5 then this build becomes a great small mana back door. Simple when a wave of minions come Void Ooze to reduce all but the tank minions to half health and your AD and AS should farm the rest. And your AD and AS can turret kill in 10 seconds or less (Assuming that minions get there and whip your minions to force you to flee). This is great in case you are ganked because you save all your mana for the gank (and if you see it coming you just need to step out of turret range for a sec to prepare).

If Void Ooze can't be leveled then level Caustic Spittle, this is for dealing with 1v1/1v2 targeting everything on one foe at a time.

The next priority is the Ult. Because the Ult uses AD and AP this build is perfect for it. The ult really puts the hurt when fighting champions and is the reason why you save up mana by not using abilities on minions(not even the super minions).

Bio-Arcane Barrage is last to build because of the nature of who you fight. Usually the champion will stand on top of you so your range matters not. Even if the champion is ranged you are probably in range as well and can unleash everything on that champion with out increasing you range.

The items give this build its name. All of these items are depicted as swords and are all in the Ability Power section. These items are the best because each one gives AP and AD/AS. This are also in order of cheapest to most expensive, but by the second item you should be able to farm almost every minion in a lane.

The following is each item and the reasons for it.

Malady: AP, AD, Magic damage
Guinsoo's Rageblade: AP, AD, Passive AP and AS
Nashor's Tooth: AP, AS, cool down reduction
Litchblade: Mana, AP, Adds AP to AD
Hextech Gunblade: AP, AD, Lifesteal, Spellvamp (this makes all fights and fending off super minions easier)
Trinity Force: By now you pretty much have all you need and this just adds to everything (tip build from zeal)

Teleport is recommended for surprised back dooring. When the enemies are pushing and the leave minions pilling up on their turrets (usually an inhibitor turret or the one before it) ignore what they are doing and teleport to your minions. Even if they are crushing your allies and/or turrets the threat that you can do it twice or thrice as fast usually pulls them all or some away to gank you, leaving the rest for your team mates to easily kill.

Clarity is recommended for early mana problems. Over all Kog'maw will run out of mana fast and you need it to compensate for no mana items (except Litchblade). Later in the game this is needed less and less. But occasionally after a 1v1 you are at half health and no mana. Enemies try to finish you off while you can't use your abilities. This acts as a lure for the miniute they get in range use clarity and crush them leaving you with little health (which you then should recall as fast as possible).

By mid game Kog'maw should have enough AP, AD, and AS to farm all minions with little or no exception.

Pros:
1v1
1v2
Farming
AS
AD
AP
Cons:
Can't run
Can't Chase