Proof-of-work consensus works without a target inter-block time, difficulty, or even a timestamp.
This is called ‘continuous’ or ‘dynamic’ POW.
The key security property remains the same: Barring a 51% attack, the probability that a transaction which has been confirmed gets un-confirmed (or reorganized) drops exponentially with time. 
A regular (light) client still works the same way. It chooses the chain with the most cumulative work.
Miners play a betting game with their hash power remniscient of CASPER proof-of-stake.
A timestamp is only necessary when there is a fee subsidy, which should be a function of time, not block height.
A weaker version of this conjecture requires each block have at least 2/3rds of the difficulty of the previous block (numerically less than 3/2 of the previous work).
 More precisely: If a transaction has been seen in the best header at wall clock time
t0 and that header is buried under some later header at wall clock time
t0+t in the best branch at wall time
t0+t, then the probability that it gets rejected or reorganized in the future drops exponentially with time, as a function of