A semicolon is different than a period in that it carries the connotation that the adjacent clause is a continuation or modification of the idea introduced by its immediate predecessor, not a separate thought (regarding the same topic, lest a new paragraph begin).

I don't think it has much to do with the commonality of the glyph in code, where ; usually represents a conclusion, not a continuation. It may simply be that coders and/or internet-savvy readers have more exposure to writing that utilizes semicolons and they obtain the habit by osmosis.