zocken
to game
Colloquial for playing video games or computer games intensively, often over a longer period of time.
Am Wochenende habe ich mit meinen Freunden die ganze Nacht gezockt.
At the weekend, I gamed with my friends all night.

to game / gamble
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to game
Colloquial for playing video games or computer games intensively, often over a longer period of time.
Am Wochenende habe ich mit meinen Freunden die ganze Nacht gezockt.
At the weekend, I gamed with my friends all night.

'Zocken' is a colloquial word in both meanings. In formal contexts, you would instead use, for example, 'Computerspiele spielen' (to play computer games) or 'Glücksspiel betreiben' (to gamble).
Er zockt am liebsten Strategiespiele am PC.
He likes gaming strategy games on the PC best.
The context reveals whether video games or gambling is meant. Words like 'Konsole' (console), 'online', or 'Computer' point to video games. Words like 'Casino', 'Geld' (money), or 'Poker' point to gambling.
Wir haben online bis tief in die Nacht gezockt.
We gamed online until late into the night.
In the context of video games, 'zocken' is often used without a direct object. Typical phrases are 'eine Runde zocken' (to play a round), 'mit Freunden zocken' (to game with friends), or 'die ganze Nacht durchzocken' (to game all night long).
Lass uns am Wochenende eine Runde zusammen zocken!
Let's game together for a bit at the weekend!
When it is about gambling, the stake is often expressed with the preposition 'um' plus the accusative. The activity itself is often described with 'beim' + dative.
Sie zocken jeden Samstag um kleine Geldbeträge.
They gamble for small amounts of money every Saturday.
to play
'spielen' and 'zocken' can both mean that you are playing a game. 'spielen' is neutral and fits board games, children's games, video games, and also gambling. 'zocken' is colloquial and usually refers to playing on a computer or console for a long time or very intensively. It can also mean gambling with risk. The words can be confused because both fit with games and gambling. If you want to speak neutrally, use 'spielen'. 'zocken' sounds more casual and often a bit stronger.

Paul zockt am Wochenende oft mehrere Stunden mit seinen Freunden online.
Paul often games online with his friends for several hours on the weekend.
Am Abend spielen wir mit den Kindern ein Brettspiel.
In the evening, we play a board game with the children.