What do you call the sequences of letters that produce phrases when read letter by letter? Examples include "CU" for "see you", "IC" for "I see" and so on.
While we may tend to think of an abbreviation as a shortening to the first part of a word (abbrev for abbreviation), it can be defined as
a shortened form of a written word or phrase used in place of the whole
Wikipedia has this to say about "Textese" in particular:
Widespread use of electronic communication through mobile phones and the Internet during the 1990s allowed for a marked rise in colloquial abbreviation. [...] SMS, for instance, supports message lengths of 160 characters at most [...]. This brevity gave rise to an informal abbreviation scheme sometimes called Textese, with which 10% or more of the words in a typical SMS message are abbreviated.
Of course, there are many types of abbreviations, but, broadly speaking, "txtpsk" is an abbreviating act.