TL; DR: It's possible to get Dug without the Kingdom Pass, but takes constant work at the game.
I'm another player who did not purchase the Kingdom Pass, and at least as far as it appears on Reddit I must be one of the very few who was able to get Dug without buying the Kingdom Pass. I'm probably up to about level 154 right now after completing the event. I completed every single happiness-producing task during the course of the season (daily, weekly, event, collection leaderboard, etc.) I did buy each premium character with gems, I don't recall there being any premium buildings (outside of the Kingdom Pass), but I bought it with gems if there was one I am not remembering. But, I otherwise spent no gems other than maybe 8 per week swapping out 1-2 weekly tasks per week, nor used any of the time-skipping things that I find mostly useless and have I think like 2,000 of.
My goal with this season was to find out if it was possible to get Dug without the Kingdom Pass, and I can say that it was, at least for me; and also to determine if that is something I wish to continue doing. I've always played this game more than I should, so I didn't have to alter my playing style very much for the season, other than swapping out weekly tasks Thursday mornings and starting a ton of 6-hour tasks and whatever. I pretty much can't stand Thursday mornings under the season system. But, since I didn't alter my style all that much, I will probably continue and hope the next season doesn't get any worse, and just continue to decide on an each season basis. For me, Charles and Paradise Falls and whatever else weren't worth $20 to me (same as the one Star Wars attraction I don't have, a shuttle or something, when that was made available for purchase a few months ago). Those are the only items I don't have in the game.
On the other hand, there are tons of people on Reddit asserting it's impossible to complete the season without the Kingdom Pass; that they completed every happiness task during the season "except for 1 or 2 weekly tasks", and they are only level 139 or 140 or so, or worse, and won't be able to get Dug. My experience does not reflect that, I was able to complete the season with over a week left, spending no money or gems other than premium character purchases. I suspect nearly all of them are likely understating the amount of happiness tasks, in whatever form, that they didn't complete, based on my own experience, but I guess there's no way of knowing. Many people seem to think there must be a bug with the happiness system, which I suppose I wouldn't be surprised with Gameloft if that were the case, but I saw no indication of that myself and happiness seemed to add up correctly each day for me.
Sorry this is so long, but it's a non-Kingdom Pass perspective for whoever cares.