Bad accounting - yes when the particles are moving faster in one direction they will have greater mass, but to get them to move faster in that direction you need to push them first, imparting that momentum while creating an equal and opposite reaction on the thing accelerating them, in this case the ship. Unless you can find something external to the ship to accelerate the ions (in which case this becomes nothing more than an ion sail), you're not going to get any thrust.
More generally, neither the ability to "reach 99% of the speed of light" nor even being propellant-less are that impressive, and anyone touting such properties doesn't know what they are talking about. Technically a flashlight is a propellant-less engine capable of accelerating you to 99% of the speed of light if you are willing to dump enough power into it. According to the article, even if this did work, "it would need to generate 165 megawatts of energy to produce 1 newton of thrust." Now a nuclear reactor capable of generating 186 MW would have a mass of approximately 140 tons, meaning it would take a little over 1 million years for the drive it was powering to reach 99% of the speed of light, assuming every other part of the ship had zero mass. For comparison, we've already successfully built and tested in space beamed laser propulsion systems capable of producing thrust at 143 kW/N, over 3 orders of magnitude better, which is just as propellant-less, and in fact since the power source does not need to be on board, its rate of acceleration is not constrained by power density of a reactor.
This story is three years old - so no idea why this click bait site is reporting it as new. The link to the NASA paper in the first paragraph of the article is a broken link. The paper itself was first published in 2019.
Relativistic craft are expected to have some type of whipple shield substantial enough for the debris undergoing nuclear fission on collision
That being said there are problems before that need to be addressed, frankly that it violates the laws of thermodynamics; "Burns notes the efficiency problem in his presentation, and also adds that his work hasn't been reviewed by experts"
Any craft using this engine would remain stationary. This is just another regurgitation of the emdrive concept except with ions instead of microwaves. They even re-used a rendering of the emdrive.
I don't know who decided to use the EMdrive illustration on this, the paper uses a different concept altogether. Whereas the EMdrive bounces RF around to "achieve thrust", this uses charged particles in a helical beamline... the tricky bit is to efficiently transfer 165 Megawatts into a beam to accelerate it, then couple that power back out to recover it. Needless to say, there are some stiff engineering challenges involved. ;-)
More generally, neither the ability to "reach 99% of the speed of light" nor even being propellant-less are that impressive, and anyone touting such properties doesn't know what they are talking about. Technically a flashlight is a propellant-less engine capable of accelerating you to 99% of the speed of light if you are willing to dump enough power into it. According to the article, even if this did work, "it would need to generate 165 megawatts of energy to produce 1 newton of thrust." Now a nuclear reactor capable of generating 186 MW would have a mass of approximately 140 tons, meaning it would take a little over 1 million years for the drive it was powering to reach 99% of the speed of light, assuming every other part of the ship had zero mass. For comparison, we've already successfully built and tested in space beamed laser propulsion systems capable of producing thrust at 143 kW/N, over 3 orders of magnitude better, which is just as propellant-less, and in fact since the power source does not need to be on board, its rate of acceleration is not constrained by power density of a reactor.