I must admit, I missed this at first. The appointment of 16 additional cabinet ministers and the cutting political funding should not be viewed as contradictory policies. They should be looked at as component pieces of a common policy.
Think about it. 16 new cabinet ministers mean 16 newly staffed cabinet offices. Although the employees in these offices are technically government employees, the work they do is generally highly politicized and they are in essence working for the governing party. In other words, they do the work that party employees would otherwise do.
So, when the Tories cut direct funding to political parties, they are cutting it from everyone except themselves. They still get their money from government coffers. Its just comes in through the back door.