Relevance of change in Inventory in calculation of Free Cash Flow
When you manufacture a product, you incur some production cost. However, you do not account for this production cost in the $\text{Cost}$ line of the income statement until you actually sell the product. While the product is sitting in your inventory waiting to be sold, you have already incurred some (actual, monetary) cost that is not visible in the $\text{Cost}$ line. That is why you have to adjust the reported $\text{Cost}$ by $\Delta\text{Inventory}$ to obtain the actual, monetary cost for the period. 

This is why $\Delta\text{Inventory}$ belongs in the FCF calculation.