Is there a term to describe this kind of strikethrough?
No, I don't believe there is.. it's simply referred to as a revision, edit, strike-through, or retraction.
And yes, this is seen everywhere on the Internet today. IMO, this usage of a strike-through is somewhat analogous to how people use hash tags, but with the scope of the expression being much more immediate; a kind of way to comment on a statement while it's being made, whereas hash tags comment after the fact.
That being said, strikethroughs occur before the associated word/phrase, instead of after, which is in contrast to an epanorthosis (mentioned in a comment). The two have a similar effect on the reader, however, a strike-through is an independently existing comment pertaining to what's next to be said, and is presented in the form of an explicit retraction. An epanorthosis, however, is dependent upon the most previous statement, and, serves to refocus/correct/enhance what had just been stated.
A post has been made here regarding the differences between a strikethrough and an epanorthosis.
An answer has been provided for that post, in which the potentiality of any differences in use between strikethroughs and epanorthoses is brought into question, and the general consensus is that the two should not be regarded as the same, and that they have fundamental differences in usage.
Given this, I reinforce my response to the OP.