chechtaHghach isn't just inebriation; it's ongoing inebriation. If we pretend for a moment that we didn't need a suffix between the verb and -ghach, how would the following sentence be any different? joch chechghach 'Iq.
I think this is a -ghach with a -taH in there only because the translator wasn't allowed not to have it, which is not how -ghach works.
How does this idea fit with: http://klingonska.org/canon/1994-09-holqed-03-3-a.txt ? Drunkenness, inebriation, or "continuing" drinking?
I'm not sure I understand the question. Okrand explains that you basically don't use -ghach without another suffix between the verb and the -ghach. This Duolingo sentence seems to want to turn chech into a noun without that intervening suffix, but to satisfy the usual -ghach rule they're throwing in the least-meaning-changing suffix they can find, -taH. But chechtaHghach means ongoing inebriation, not just inebriation, and that isn't what the English sentence is asking about.