In the activity theory paper, the author presents an example of “Mark is driving to Aunt Sally’s house”. So Mark has an outcome or motivation to reach Aunt Sally’s House. To achieve that outcome, he does a number of activities like calling up Aunt Sally to inform her, checking weather, printing directions, driving to the destination etc. So, if I try to fit the Hammering/Hammerness theory into the Activity theory. Hammering would be each of the individual activities that the user performs. In order to achieve each of these activities, he makes use of various tools (Hammers) like his mobile to call up Aunt Sally; using local newspaper to check weather; using his computer, printer, internet, Google Maps to print directions; his car to drive to the destination and so on. And Hammerness would be the properties of each of these tools.
As I interpret it, Heidegger’s main argument is that we humans, give priority to the act of doing/activities rather than concentrating on the Hammerness or the properties or the reality of the tools that we use to do those actions.
P.S. Here, I am using the words actions and tools in very broad sense. Actions dont just mean physical actions that we do, but thinking about something is also an action.