The ELI is a great piece of engineering. The amount of power it outputs is indeed really insane. We could compare it with a large solar flare in terms of the energy that it provides.
However there are a few key factors which have to be taken into consideration, similarly to what was discussed in relation to the LHC.
#1. The title is very misleading: "
World’s most powerful laser could ‘tear apart the vacuum of space’" because to the untrained mind this means that they will build a laser and then shoot it into outer space, which is totally false. The laser will be fired in a chamber probably no bigger than your average coffee cup, which was voided in advance. This is similar to the LHC situation, where the case was that people imagined that the huge magnets that power the particle accelerator were actually of average wall thickness, and a huge ray of light is passing through the middle of them. This is very false, because the particles travel in a very small "pipe", of a few millimeters in diameter.
#2. At the LHC the biggest paranoia invoked was the creation of mini black holes, which would grow and eventually eat us all. All the scientists at CERN quickly explained why this is not only incredibly idiotic to assume, but even if it were the case of a mini black holes being created, they would be under the critical mass. This means (and was proven) that the particular black hole will devour itself and disappear. In the case of the ELI this is not an issue at all. The issue here will most likely be related to not being able to stop the laser once it's started - a retarded assumption to say the least. The laser will be active for A TRILLIONTH of a second, similar to the LHC impacts which happen also for similar durations of time. Yes, this amount of time is more than enough to gather any needed data.
#3. "This veritable death ray won’t be used to further the aspirations of an evil genius — at least, that’s not its purpose." Oh damn it... This is NOT a ray, nor is it something you can point and shoot. This will be a huge installation of devices with it's peak in a small chamber of testing where the laser is shot. Every other device around is just a necessary tool, and due to the incredibly small scale at which we are working every calibration must be done within nanometers, if not picometers. Hence, not only can you not move the laser, but it fires in a sealed chamber and most likely not one human being will be allowed in the area of the device when testing commences.
#4. Another idiotic idea that people might have is related to the fact that the laser must gather power. When people think gather power, they imagine energy being pumped into some tanks or something, and then into the laser. Naturally they become worried that the storage of that power might explode and destroy a bunch of shit... False. The power has to be injected indeed, but amplification is usually done by mirrors and optical "tricks" to focus and energize the laser beam. Initially it will be split up into 10 pieces or so, parts which will be amplified individually and then "merged" into the highly energetic final beam.
In case you're curious what they are trying to discover, I refer you to
this post. By firing this laser they are hoping to witness very small particles "drifting" away into these "hidden" dimensions. A law of physics (Conservation of Energy) states that the amount of energy you put into a process is equal to the amount of energy coming out of the process. "Everything is converted, nothing is ever lost". This means that the amount of energy they put into the experiment must be equal to the amount coming out, however if the laser causes certain very small particles to "hide" in these extra dimensions, then the amount of energy they measure at the exit will be smaller than at entry. This would offer quite strong proof that M-theory is, at least partially, correct; and that indeed everything you see around you is created by tiny filaments of energy vibrating at different frequencies, vibrations which are defined by the shape of the "hidden" dimensions.
This same idea was tried at the LHC, however until now the results have been inconclusive both in confirming and in in-firming M-theory. They were hoping that the impact of particles might create "debris" (read as other smaller particles) that will hopefully "hide" in the 5 extra dimensions of space.