Perhaps an unpopular opinion, but I actually like D&D and much prefer it to every other family of games I've tried (WoD, GURPS, PbtA, etc). What i dont like is the current iteration of D&D, which is why my recommendations are:
Swords & Wizardry Complete: it's OD&D with some of the rough edges sanded off and all the optional material added. Tons of classes, lots of tools for procedural world building, and very easily hackable. It's simpler to teach to a new player, and its more flexible than 5e for experienced players. The tick-tock of the dungeon turn structure makes it easier to keep pace as a GM, and when in doubt, rolling x-in-6 always holds up. If you want a classic dungeon crawler, this is it.
Whitehack: Still D&D but more narrative. Skills are replaced with groups that can give advantages to tasks directly influenced by membership in that group. Magic is super flexible and everyone has access to some form of it, but the "magic user" class gets to just make up their own spells and pay some HP depending on effect size. Great rules for base building, good GM advice for making adventures that aren't dungeon or wilderness crawls (but are structured like those things). The core mechanic minimizes table math so even your players who struggle with addition can play fast. Less deadly than actual old D&D but keeping the same vibe. It's my favorite for those who prefer narrative to mechanics. In a lot of ways, it's D&D rewritten for the way a lot of people actuslly play 5e.
Short version: No, not every game has target numbers.
Long version: within the d&d context, DCs set by the DM have only existed for about half of d&d's history, starting with 3e. Before that, "skill checks" worked in a few different ways including percentile dice compared to level, rolling under the most relevant ability score, or just rolling a d6. Outside the d&d context, my gut says that arbitrary target numbers are less common than fixed ones or ranges. In my experience, they're faster and simpler, too.