Chase - might need a bit more info here to advise you properly. How long passed between both episodes? When OW text came through, was it from the same number as last time or did it show her name (or codename)? That is, were you able to establish that her number had been deleted from his phone? Did you ever see what your DP was sending her? Also, how did he "close" contact with her last time? Clearly not emphatic enough for her not to text again.
What I find strange you see, is that when she got a reply from "him", she didn't express delight that he had responded - and launched straight into explicit messaging. Most people would want some kind of build up to that after a break. Would have been normal if the text you found in this most recent episode had said "How how are you, been thinking of you lately" but to start with a suggestive text doesn't quite add up.
The signs of an affair are many and varied and the signs my DH was displaying did not accord with anything I'd believed before.
What ever happened, I suspect you don't yet know the full story. I'm not suggesting that anything physical has actually happened yet, but in answer to your initial question, yes of course it's cheating.
If it helps, the start of my DH's affair with OW was a bit like this. She played him a bit more carefully though. The initial bout of texting and E mailing was fairly innocent, but full of stuff about how wonderful and handsome he was etc. She repeatedly asked to meet up and he kept saying that "it wasn't a good idea". So she gave up for a while. Had I found out that this was going on at this stage, I feel sure my DH would have deluded himself and me that this would never have progressed to an affair and that he had "done the right thing" by refusing to see her. But of course, this would have been utter bollocks (and I hope I would have seen this at the time.)
The truth was that as adults in monogamous relationships, we know instinctively that text relationships with people who want to have sex with us, that are secret from our partners, are wrong. My Dh would have probably acknowledged this, but he absolutely wouldn't have acknowledged what HE was getting out of it. And that by engaging in it in the first place and being so half-hearted in his refusals, what he was doing was laying pathways for her to return and try her luck at some other stage. This is why your DP's "closure" with her last time is important.
In our case, I hadn't a clue about the first batch of texting and E mails, or that he was in contact with anyone. I do know that at this time, I was feeling very uneasy about something, but put it down to all sorts of things other than that - it would have been the very last thing I would have thought of. Perhaps you had a better antennae than me, hence you found out the first time - might help to tell us what that was?
Months went by and my DH's OW got back in contact with him - and it took another month of intense (in volume) texting for her to show her hand about what she really wanted. Her cue for that was my DH agreeing to meet her, but neither of them was showing their hand up till then. As soon as she did, my DH entered into the whole thing with gusto - the "pretence" had lifted, you see.
Had I found out at this point, my DH would have had a lot more explaining to do, but would have insisted that he never had any intention of following through with the arrangement and that this was just a fantasy. Which again, would have been utter bollocks.
Unfortunately, I never found about any of this until it had become a full-blown affair.
The point I'm trying to make is that when it's at this texting stage, men often delude themselves that this is not infidelity, as they haven't had sex...yet. But the truth is, boundaries are being crossed and barriers to infidelity are being dismantled all the time. It doesn't necessarily occur to them that something must be seriously wrong for them to be doing this. They never seem to acknowledge that they are getting something out of this and will hide behind the "she was pursuing me" line. This is a smokescreen. The truth is, they are taking an active part in this for a reason.
What ever you do, get to the bottom of this and force your DP to confront what was really going on here. Don't accept smokescreens and delusions. There's a book I'd recommend called "Not Just Friends" by Shirley Glass that explains all this, but I urge you to get to the root of it, or it will absolutely happen again. Delusions and smokescreens do not "affair-proof" a relationship - and stopping the behaviour is like putting a band-aid on a wound that needs stitches.
Would suggest counselling (all counsellors seem to have read the above book) if you need a third party to get him to acknowledge all this - and just a trawl through this site will tell you all you need to know.
These texting relationships are NEVER harmless.