The IS-LM model stipulates certain “channels” of influence that one variable has on another. These stipulations are Keynesian and therefore subject to critique from an Austrian viewpoint.
Keynes asserted that the interest rate is determined by the stock of money and the demand to hold money. This effect occurs indirectly as people trade money holdings for bonds in their asset portfolios. People sell bonds to satisfy their demand to hold more money and therefore, interest rates rise as the necessary consequence of bond prices falling.
Austrians counter that as a medium of exchange people hold money in lieu of demand for goods in general and not just bonds. People sell across all goods to satisfy their increased demand to hold money and therefore, prices in general fall.
Furthermore, unless time preferences change during the transition between the original and higher demand for money, the ratio between consumption and saving-investing will not change. Time preferences determine both the pure rate of interest and the ratio of consumption to saving-investing. It doesn’t seem to me that the unnamed author provides an argument to show that time preferences necessarily change in the transition. He has simply stated, correctly, that the composition of investment will shift away from other goods and into commodity money. But commodity money production is no different than the production of any other good in the economy in terms of generating a rate of return. And so, his case is no different than increased demand for smartphones leading to an increase production by pulling capital and labor out of the production of landline phones. Such changes in the composition of investment do not affect the rate of return or the proportion of resources in the economy devoted to saving-investing, both of which are determined by time preferences.