In 100% literal RAW for One D&D as of right now, monsters would crit.
If you insist on playing the playtest in full rules-lawyer mode, rules for monsters would have to come from the 5e DMG as we have no other available rules.
As quoted in the question, rules for One D&D players say that players can crit and imply that monsters don't but do not explicitly say that. Old 5e rules do explicitly say that monsters can crit, and we have to use those old rules as part of our ruleset or we have no rules for monsters.
Explicit beats implied, especially as there is no actual contradiction in the rules-as-written (even if the rules-as-intended contradiction is perfectly clear), therefore monsters can crit.
There's one big problem with this, though: we based all of the above on the assumption that we are playing by 100% literal RAW, and:
100% literal RAW play is officially declared to NOT be supported by the One D&D playtest
A sidebar on the first page states:
This article is presented for playtesting and feedback. This D&D material is in draft form, usable in your D&D campaign but not refined by full game development and editing. It isn't officially part of the game.
What that means is that errors and inconsistencies are expected and inevitable. When playing the playtest one of your jobs is to look out for those inconsistencies, try out methods of resolving them, and provide feedback to WotC on how they can best be resolved. That is, in fact, the whole point of a playtest.
Once we take this into account, it is clear that:
The 'correct' way to play the playtest (in so far as one exists) is for monsters NOT to crit
OK, we've found an inconsistency and we're supposed to deal with it like rational adults rather than going full rules-lawyer over it.
In this case, the way the actual One D&D material (not the previous edition material we're using to fill gaps) is clear: crits are a special mechanic for players. The only evidence to the contrary is in material we know is going to be rewritten soon, so there's zero reason to treat it as holy writ.
Conclusion: One D&D monsters don't get crits, that's a player-only mechanic.
Absolutely, if you want to try something else you're welcome (and encouraged!) to play around with modified versions of the rules. House rules have always been an accepted part of D&D, and that goes double for a playtest.
But if you're trying to play 'true' One D&D, until and unless a One D&D text indicates that monsters can crit, they don't.
For any readers who do play strict RAW, please note that the above isn't meant as a criticism of that playstyle in general. It's not my style, but as long as you're having fun, more power to you.
I will, however, stand by the claim that strict RAW play with an unvetted playtest is a terrible idea - the sane 'strict RAW' approach to One D&D is: 'this is still broken; I'm going to stick with [insert edition here] and check back later when WotC have had more time to iron out the bugs'.