Not very sure I do either, but I'll have a go.
Presumably the MPs didn't realise they weren't allowed to spend their business costs budgets on the NRG. They believed this bit was permitted by the regs.
However they knew they weren't allowed to spend their business costs budgets on political campaigning (IIUC).
IX Wireless wanted to fund the NRG covertly.
So they came up with a scheme where they all benefitted.
The MPs' offices paid money from their business costs budgets to the NRG, so the NRG benefitted and IX Wireless benefitted by not appear as a donor to the NRG.
IX Wireless then gave the same amount of money to the MPs' offices, which may have been described in the accounts as political donations. So the MPs benefit because they now have the same amount of money to play with as before, but can now use this money for election campaigning instead of just for office costs.