The first strategy is to invest in domestic equities; foreign developed market equities; property; commodities; bonds and cash. The second strategy is to invest in domestic equities; property; foreign developed market equities and emerging market equities.
You are correct to state that the first strategy would have a lower volatility – this is because it has allocations to various non-equity and non-correlated assets. It would be interesting to see what is the volatility of the second strategy. I'd guess it's higher than the first, as it is, in effect, an all equity (except for property) strategy.
If you go for equal allocations to each asset class, which both strategies appear to recommend, you, or more correctly the developers of these strategies, are basically saying that the efficient frontier, i.e. the combination of assets that gives you the maximum return for a certain level of risk, is a load of codology. If this were the case, an investor would go for the second strategy as he/she would appear to be unperturbed by risk. However, if you are risk adverse, as rational investors are assumed to be, you would go for the first and in addition to equities, allocate to non-equity asset classes that are not perfectly correlated with equities.