There are various reasons people sometimes drop certain ‘leading’ pronouns or articles. I wouldn’t presume to know if that’s the case here or not, but I don’t think the missing “it’s” is either (a) done to annoy a few message board posters (it’s hard to imagine Drew would feel the need to tick off a handful of people nor that he would pick something trivial in the grand scheme of things), or (b) “laziness.” The mind can play interesting linguistic tricks on people.
For example, and I’m not saying this is the case, but just the kind of an cases I studied in communications classes, if a person was exposed to a variant of a common expression (like “It’s in the bag”) in their youth that was slightly different (say one’s family used the different phrasing or it was a local colloquialism), then as an adult there’s a strong tendency to use the phrase as you knew it. As a youngster, I apparently misread or mispronounced the word “epitome” as if it rhymed with “dome” instead of the long 'e' sound. To this day, many decades later, no matter how many times I see the word, my brain processes it the wrong way. I don’t know what I would do if I was on TV—I’d need some kind of serious help not to revert to saying it the wrong way if I saw it on a prompter even though I’d say it correctly if I said it without a visual prompt. The brain can do funny things that have nothing to do with laziness. Again, I’m not saying that’s the case, just trying to point out that things are sometimes are not conscious choices. And when we’re talking about a relatively minor thing like “it’s” before “in the bag,” it may not be a big issue.