This bonus system has been first introduced by MICROGAMING casinos. Other names are 'the eZ bonus' or 'Flexi system bonus'. Summarized in a few words: the bonus is incrementally converted to cash! Most Microgaming casinos use the Clearplay bonus system!
The ClearPlay system 'counts and displays' to players what is available to withdraw and what still has a play-through requirement (= must be still wagered). Your account is split into a separate 'cash balance' and 'bonus balance'. While playing in the casino, the 'bonus balance' is converted to the 'cash balance' in 10 credit increments.
All games are allowed, but games are weighted at different percentages. High house edge games like slots count 100% towards the wagering. Low house games like Blackjack and video poker contribute less towards the wagering. You can withdraw your cash balance and bonus winnings at any time, whether you have completed wagering or not.
Unfortunately, many casino groups use a modified form of the bonus where you must complete the full wagering before making a withdrawal.
Unfortunately not all software operators are offering this sort of a system within their software. Anyway: MICROGAMING casinos do!