The very same link sheds some light on that question too:
"Time magazine reported that throughout 1981 and 1982, the Israelis reportedly set up Swiss bank accounts to handle the financial end of the annual multi-million dollars arms deals between Iran and Israel during the Iran–Iraq War."
The vast majority of arms dealing is state-controlled, all terrorist groups combined aren't big enough to make a dent.
And in any case, the original claim was "money laundering for terrorism" not the other way round.
Notice how original claim was "launder a lot of money for terrorism" as if it was something well-known, widespread and repeated. However the evidence so far is "how about this" and "how about that". I would appreciate something more specific like "the investigation found X billions laundered for Hezbollah".
Regarding your question: the whole concept of "terrorist states" is made up if you ask me, and UN agrees. States wage wars and commit war crimes (or "collateral damage" if you win the war), other states retaliate. This has little to do with the asymmetric confrontation with terrorist groups which inflict violence but then evade retaliation due to their secretive and decentralized nature. States can't do that: they are centralized and not secretive, you can find them on the map.
I checked your links and the word "terrorism" isn't mentioned once. There a single mention of some Al Qaeda members having accounts but it's pretty far from "proof of financing terrorism".