I read those articles in your links.
There is a fair amount of difference between them and a pipelauncher..
The various kind of superguns are essentially something that replaces rockets, whereas a Pipelauncher is something that assist rockets.
Though it wouldn't be practical, one could "launch" a 747 jetliner from a pipelauncher.
In terms of similarity in function, a pipelauncher is more like the launching catapult on aircraft carriers.

The advantage of launching rockets from a pipelauncher in my view of the priority is:
It serves as cheap launch pad- comparing it to launch pad on land or launch pads on the water. Ocean covers more than 70% of surface area of the world. One could launch from any latitude, but the most efficient location is at the equator. This is particularly true if the destination of the payloads is in Geostationary orbit.

And pipelauncher would work in terms of being economical in an environment in which there were a few launches into space [as in the current environment] and work well in environment in which there were a large amount of rockets being launched.

A pipelauncher is NOT so much about adding speed as allowing rockets to get to a higher altitude in a shorter period of time. Therefore a pipelauncher main advantage in regards to adding speed to a rocket is getting rockets to an altitude in which rocket engines perform at higher efficiency and there is less atmosphere to that resists mach speeds.
As I roughly calcuated somewhere in this thread, launching a rocket at 150 mph is roughly equal to launching rocket from 10,000' high mountain.

The time rocket takes to get to 60,000' or 100,000' can be shorten. If it takes a rocket 60 seconds to reach around 60,000, 150 mph over the time of 60 second adds 13,200' in elevation. If rocket is accelerating at average of 30' per second per second over period 60 seconds that acceleration gets it to 54,000'. If rocket has slower acceleration during first 60 second, the pipelauncher added 150 mph is more significant and obviously if rocket has a much faster acceleration during first 60 seconds, the added 150 mph is less important.

Another thing you can compare to the added speed that pipelauncher adds to a rocket are solid fuel boosters. Solid fuel booster [known as zero stages] generally use up their fuel in a short period of time- and their purpose is also to get the rocket higher in shorter period of time.

The Shuttle of course has huge solid boosters, their burn time is 124 seconds. The Shuttle solid booster provide a huge amount thrust, they also provide a very bumpy ride.

At Shuttle lift off:
"Liftoff Thrust: 25 751.600 kN (5 789 190 lbf). Total Mass: 2 029 633 kg (4 474 574 lb)."
http://www.astronautix.com/lvs/shuttle.htm

So the shuttle has 5,789,190 lbf and weighs 4,474,574 lb.
Which means if the Shuttle only had 4,474,574 lbf it would be able lift it's weight but not accelerate. So it has 1,314,616 lbf which is accelerating it. If the Shuttle had 4,474,574 lbf which accelerating [8949148 lbf at liftoff] it would accelerate at 1 gee, if it had 2,237,287 lbf accelerating it, this would be 1/2 gee acceleration, the shuttle instead has over 1/4th a gee and less than 1/3 a gee at lift off [9.4' per sec/sec].

As fuel is burnt the weight is reduced and with same thrust you get a faster acceleration. And also as you get thousands of feet higher in the atmosphere with in less atmosphere pressure the rocket engine increases their thrust [they get better "gas milege"- more power with same amount of fuel used].

The Shuttle's solids use all their fuel in 124 seconds, so roughly, in 25 second, the solid lose 20% [1/5th] their mass. Each of the two boosters weigh 1,299 990 lb, so both weigh 2,599,980 lbs. About 519,996 lbs is shed. So around the 25 second mark the 4,474,574 lb starting weight is more than 1/2 million lbs less. So Shuttle weighs at 25 seconds somewhere around 3.8 million lbs. Still having around 5 789 190 lbf of thrust, so at this point it has about 1,999,190 lbf accelerating it. If it had 1.9 million lbf accelerating it would have 1/2 gee, so somewhere around 25 seconds after liftoff the shuttle is accelerating around a 1/2 gee.

And at some time in about 60 seconds the shuttle is going to reach 1 gee in acceleration. BUT if a vehicle were to have a constant 1/2 gee accelerate in the first 60 second, it would reach a higher elevation compared to Shuttle's delayed time before it reached 1/2 gee and faster.
As follows:
In first 20 seconds at 16' per sec2, you get 3200' and a speed of 320' per second
Compared to:
In first 20 second at 10' per sec2, you get 2000' and a speed of 200'

In first 40 second at 16' per second per second, you get 12800' and 640' per second.

If we give 16' per second to the 20-40 second period:
10' per second for 40 seconds, get 8000' and 400' per second. Plus 6' per second for 20 seconds for distance of 1200' and 120' per second. Giving total of 9200' high and 520' per second.

In 60 second at 16' per sec2, you get 28,800' and 960' per second.

At 50 second point [halfway between 40 and 60 seconds]
the shuttle's mass is about 3,413,834 which leaves 2,375,356 lbf, so averaging acceleration could be 22' per sec2.

10' per sec2 for 60 sec, get 18000' and 600' per second, plus 6' per sec2 for 40 seconds gets 4800' and 240' per second. Plus 6' per sec2 for 20 gets 1200' and 120' per sec.
Total of 24000' high and 960' per sec.

Not by any plan on my part but at the 60 second point both the Shuttle and constant 1/2 gee acceleration is going at the same speed though at different altitude and different acceleration.
This an advantage/aspect about adding speed at beginning of launch phase- it gets the rocket higher before the rocket starts to gain a lot speed while still in denser atmosphere. On Shuttle launch this "problem" is called Q-max wherein main engines are throttle back until such time as Shuttle gets to higher and less dense atmosphere.

So getting back to what a pipelauncher is. It's a launch platform which quite stable and can designed to launch rockets vertically at speeds in the range of 50- 400 mph. From a elevation of the launch of the rocket above the water of 500' to 2000'. And could have capable of acceleration rate varying from a constant 1/4 a gee up say a constant 6 gees.
A pipelauncher could be designed to launch smaller sub-orbital space vehicles [50-100 ton], standard size rocket [300-3000 ton], or even some exotic drawing board type rocket such as Orion nuclear rocket [100,000 tons- assuming the Orion would ever be politically/legally allowed to be launched from the Earth's surface].
A pipelauncher works well at lifting a lot of weigh at a fairly fast acceleration [a gee or so] for distances of hundreds of feet vertically. Having a pipelauncher accelerate a rocket at less than 1 gee and to speeds approaching or exceeding 400 mphs is possible with a pipelauncher but it's expensive, both in terms requiring a taller pipelauncher and more massive, and in terms of operational costs. A modest size pipelauncher say 1000' tall, that can lift a max of 1000 ton rocket payload at max of 1 gee to rocket launch speed of around 150 mph would use less fuel than most the rockets would use to accelerate to 150 mph.