When you have a list of similar items, start by assuming the relative clause refers to the closest target, in this case "functions". You can then use contextual cues, or common sense, to see if it should apply to any of the other items. For example:
Her basket contains apples, oranges, and other fruits that are not spherical.
The relative clause most obviously refers to "fruits", and common sense tells us it does not refer to either apples or oranges, because these are spherical.
However, in your example, common sense should tell you that processors and drivers occasionally need to be updated, and are therefore members of the overall set of "functions that need updating occasionally". It's not about the relative clause at all. Instead the structure of the sentence can be paraphrased as:
It also contains code to support [first item], [second item], and [other items in the general group that includes both the first and second items].