This guy's main real criticism is "train viaducts cost X and Musk's proposal is 0.1X therefore it must be wrong" is total bullshit. It MIGHT be valid under the following assumptions:

1. The weight of the train and the hyperloop capsules are the same

2. The construction methods employed are identical.

But they're not! Average train car weight (if they have to comply with FRA regulations) should be in the 60 ton range. https://www.ebbc.org/rail/fra.html and http://uk.answers.yahoo.com/question/index?qid=2006082807531... Average train car length is betwen 60 and 80 feet so we'll go with 80.

60 tons / 80 feet = 1500lbs/foot. In the case that a non-FRA compliant car can be used, that number SHOULD drop to about 750lbs/foot.

The hyperloop cars are speculated to be 16.5 tons and 28.5 tons each. No hard numbers on length but if you assume 3ft per passenger and 28 total (14 per side) and add a bit of room for the other stuff, you can come up with 14 * 3+15=57 feet or for three cars, 3 * 20+15=75 feet.

33,000lbs / 57 feet = 578lbs/ft.
57,000lbs / 75 feet = 760lbs/ft

So it looks like the big-case hyperloop will weigh about the same as the best-case high speed rail.

Now let's analyze the support mechanism. Trains run on rails (two of them) and they weigh ~100 lbs per foot and are around 3" wide and 6" tall. These rails need to be very precisely supported both side-to-side and up-and-down especially if the trains are going to run at 200+ MPH. For viaduct you've got to build the bridge, then put down the ties, then put rail on top of those, fasten it down, etc. Ties are in the range of 6-8" thick and then there's the ballast (rocks) which aren't light either and which are generally required to keep the ties from moving. On bridges (viaduct) you might do something newer and fancier but I wouldn't count on it here in the US. Overall you've got at least 200lbs/foot for the rails and I might guess another 500-1500lbs/foot for the ties and ballast and such. Rock weighs ~150lbs/cuft and so does concrete so if your ties + ballast are a foot thick and 8 feet wide (rails are 4'8" plus 20" extra on the sides) that's 1200lbs/foot.

Hyperloop runs in a 7.5 foot diameter tube with a 0.8in thick wall. 7.5 * 12 * pi * 0.8=226 square inches cross section. Or a foot of it has 2712 cubic inches of steel. At 0.283lbs/cu-in that comes out to be 767lbs/foot. Because it's pipe (which has excellent structural geometry) it is self-supporting and thus all you really have to do is get the pipe properly supported on top of the pylons, weld two sections together and you're done.

Here's the last part. Hyperloop cars will be at least a mile apart. That means the system can be designed to support just one of them per pylon. Train cars will be 3 feet apart, and thus the viaducts have to support 1500lbs/foot * 80 feet per car * 10 cars = 600 tons. Versus the hyperloop car weights of 16.5 tons or 28.5 tons.

So these two systems are mildly different in terms of their car weights but dramatically different in terms of the overall structural requirements and design to meet those structural requirements. Train track is heavy and train cars are heavy and trains are fairly dense (due to their length). Hyperloop cars are about half as heavy and hyperloop track is half as heavy and hyperloop support densities are only about half versus rail. 0.5 * 0.5 * 0.5 = 0.125 or 12.5% which isn't terribly far off from the 10% number that the Hyperloop is quoted to cost versus the high speed rail system.

TL;DR: Cut track weight by half, car weight by half, and total support weight by half and you get 0.125 which is suspiciously close to 0.10, the number that the article author had such a problem with.

EDIT1: formatting

EDIT2: tl;dr