Does an expiatory offering for an oath become obligatory for someone who swore, "By Allah, I did not film," while intending, "I did not film you except for this one video on this day"?

The default rule concerning an oath is that it depends on the intention of the swearer. If he intends by his oath something that the words can bear, his oath is interpreted according to his intention, whether what he intended conforms to the literal meaning of the words or contradicts it. Therefore, if your intention was that you had not photographed them before this instance, then nothing is binding upon you. This falls under the category of lawful tawriya (allusory speech) and ma'areed (equivocation). In the Arabic language, the word yameen (oath) has several meanings, including strength, swearing an oath, and a direction.