Come on. You can understand from context that Craig is talking about using "tweet" to mean "a post on Twitter", not claiming that he literally invented the word "tweet".
The word "tweet" wasn't added to the OED, just a new meaning of it.
Two entries for "tweet" (one for the verb, one for the noun and interjection) have been in the OED since 1916, with citations going back to the 16th century.