Their system can reversibly compress the plasma by energizing a coil. If the plasma acquires more energy in that time (by fusion producing energetic charged particles), the expansion stroke can return more energy to the capacitors than the compression consumed.
It's the electromagnetic plasma equivalent of a reciprocating internal combustion engine.
... except for the fact that they're claiming 95%+ efficiency in an engine type nobody has ever seen running when actual existing reactors of that type can't seem to make it to 1%, and the two types of engine you can compare this (ICE, steam turbine) have SOTA efficiencies of 35% and 48%. This seems less than realistic.
Then again, this is being done with private funds. So let them, and frankly, I really hope it works. Hell, if they wanted reasonable subsidy for this, I say give it to them.
They have been doing compression and reexpansion on plasmas for a long time. They are claiming high efficiency on energy recovery in these (non-fusion) plasmas. They can also do energy injection and recovery just by pulsing the coils around an empty vacuum chamber (or one filled with nonconductive gas).
There's nothing that should be unbelievable about this claim, and to dispute it would be to assert that they are outright lying. For short timescales where do you expect the energy to be going, if not back to the capacitors? Inductive energy storage on short time scales should be very efficient. Both the coils used and the plasma itself have sufficiently low resistivity. I think the gating technology for this was the switches.
The 1% figure you give there isn't for anything resembling this process, so I don't know why you brought it up except for reasons of obfuscation or your own confusion.