They are on to something... else than they try to claim on their site.
The paper on the actual science explains the concepts.
This is not intended to be the "holy grail", genuine antimatter drive (a photon drive utilizing gamma rays from annihilation of positron and electon; specific impulse of the maximal ${c}\over{g_0}$ and 100% mass to energy conversion), but a ion thruster, with positrons used to produce muons for muon-catalyzed fusion as source of ion propulsion (instead of electric field).
Muon-catalyzed fusion is a "cold fusion" process which, while working, was considered (similarly to many other similar) useless practically, the reason being a relatively low number of deuterium or tritium atoms catalyzed into fusion to helium, per positron, and obviously prohibitive price of antimatter-generating isotopes. In other words, the wattage of the process is minuscule, and energy needed to produce the anti-matter - way higher than the energy output of this fusion.
Still, products of the muon-catalyzed fusion are extremely hot (=fast) ions (= charged particles which can be directed using magnetic fields). In other words, it can be used for a ion engine of quite extreme specific impulse - heat of nuclear fusion replacing accelerating ions through electric field.
Unfortunately, the poor wattage problem remains. The site the asker linked provides beautiful visions, "months to Pluto, Proxima Centauri in 5 years, a craft accelerating at sustained 1g". The paper makes much more modest claims:
- the 6U cubesat that they will use to test the propulsion in space will be generating 100s of watts
- the propulsion will have delta V of 1 to 10 km/second
- Later systems will have more delta V and enable cubesats and small satellites to stay in orbit for years instead of days
- the cubesats with propulsion will enable very low orbit internet satellites
- in the 2020s if things go well they will be able to scale to 10 km/second to 100 km/second with 10-100 kilogram payloads for small probe exploration of the solar system
- Later beyond 2030, they will have regenerative isotopes for a lot more power and achieve ten million ISP and several kilonewtons of propulsive force
- could enable 1G acceleration and deceleration propulsion which would 3.5 weeks to Pluto
One significant actual breakthrough they claim to have made is production of "cold positrons" (usable for catalyzing the fusion) at a rate an order of magnitude greater than currently available, and with promise for improvement. This could indeed reduce the amount (=cost) of antimatter-producing isotope needed for this to work.
It's still a lot of very tall claims, especially for the schedule, without even a decent test article device for the thruster. It's still a viable (if not realistically near) concept for a fusion-powered ion drive, which would indeed surpass everything we have in terms of specific impulse and delta-V total. Regardless, there's nothing that would suggest thrust in newton range, never mind the claimed kilonewtons. While the energy density of the fuel (deuterium+tritium) is fantastic, the catalyst-producing isotopes (e.g $^{22}Na$) are still prohibitively expensive and must be used in macroscopic amounts to trigger release of any macroscopic amounts of energy.
(and this is just a tip of the iceberg of problems, like half-life of the fuel, powering magnetic fields to handle the high-energy ions, all the accidental hard gamma radiation from positron-electron annihilation (which WILL happen, wanted or not), and lots and lots the authors of the proposal conveniently remained silent about.)