In regards to the politician example you mentioned, "word play" tends to mean something else. In English, "word play" tends to refer to jokes or riddles that make use of quirks in the English language, similar to the Chinese use of "grass mud horse".
There are many other great answers to this question such as "obfuscate" and "convolute".
Obfuscate tends to mean more specifically that it is made difficult to understand; convolute tends to simply mean that something is made more complicated than it should be.
Another good word to use here would be "wordsmith". This is especially appropriate to use to describe a speaker who is carefully using language to not only confuse, but to manipulate his audience into thinking or doing something they normally wouldn't do, and often doing that in a sly way.
For example, a recording company executive that hates people making copies of music might say publicly, "Thieves are hurting our business when they make copies of our music." At first glance, this looks like a straight-forward statement that unauthorized copying of music hurts record companies, but upon closer analysis, you can see that he is equating copying to stealing, a notion that record companies definitely want the public to believe in.
A rational person would normally not think of copying as stealing as stealing, by definition, deprives the victim of the thing being stolen, but the above statement tends to be much more accepted.