Since there are no details, we can only speculate. There are only a few practical implementations. At the top of the list is an evacuated tube.
The linked article says it's desirable to do this without requiring a right-of-way or moving people out of their homes. So that puts the tube below ground level -- well below.
Let's say an evacuated tube, below ground level, in California, between San Francisco and Los Angeles. This really isn't going to work, because (all other considerations aside) the route crosses any number of known geological faults that are in constant relative motion -- some creep past each other, some wait and then periodically move all at once in an earthquake. You can't build a subsurface tube that crosses geological faults.
I don't think this is a practical idea. But it's a nice one in principle.
Yes, I noticed since I wrote the original, but that might be smoke. It's not obvious how the system would work without some sort of dedicated pathway that remains the same day after day. The word "tube" leaps to mind. :)
I'm not so sure about the right-of-way issue, since we are talking about a permanent structure. The case law that weakened the old "Cuius est solum, eius est usque ad coelum et ad inferos" ("for whoever owns the soil, it is theirs all the way up to Heaven and down to Hell") rule, as far as I've seen, all involved aircraft passing over land. I'd not be surprised if a court considered that case law irrelevant when it comes to permanent structures overhanging someone's land.
>However, while the Court rejected the unlimited reach above and below the earth described in the common law doctrine, it also ruled that, "if the landowner is to have full enjoyment of the land, he must have exclusive control of the immediate reaches of the enveloping atmosphere." Without defining a specific limit, the Court stated that flights over the land could be considered a violation of the Takings Clause if they led to "a direct and immediate interference with the enjoyment and use of the land."
Would a hyperloop cause direct and immediate interference with the enjoyment and use of the land? It might if it failed!