As far as I can see, the twosidedness is not referring to the chisquare test at all, but rather to the corresponding two-sided test of two proportions. The chisquare part is indeed a onetailed test, which it should be. The same kind of vocabulary is used in i e openepi.com. Some more details were covered in another comment, see http://stats.stackexchange.com/a/157005/18276https://stats.stackexchange.com/a/157005/18276.
If I am correct, then the entire discussion of when a twosided chisquare test should be used is more or less off topic. Or at least the answer to a question that was not raised, but to another question.
It's really odd that SPSS does not have a clear formulation of tests of proportions since that is such a common task. Even if a chisquare test in a 2x2 table is equivalent to a test of proportions, it would be easier to understand the output if it had been based on proportions rather than a substitute. It is also strange that they haven't included tests which are less sensitive to small samples (the Agresti-Coull or mid-P tests for example).