For someone in their first year of loss, who remains inside during Yizkor although not reading the text… Are they obligated to give Tzedaka as the text states in Yizkor?
There is no actual obligation unless you intended to pledge.
It should be noted that main Zechus for the Neshama is from the Tzedaka that the family member pledges (bli neder) during Yizkor.
צדקה – ראה שו”ע אדה”ז תרכא, יד. וכ”ה בסידור.