In British English only 'the game has just begun' would be correct if you are talking about an action that occured in the recent past but has an effect on the present moment. 'The game has just begun = the game started recently and is still in progress. This is called the present perfect tense In American English you can use both the present perfect and the past simple (the game just began) to talk about an action that occured in the past and has a present effect. 'The game just began' would only be possible in British English if you are referring to an action that was completed in the past and the present moment is not important to the meaning. But the meaning of 'just' is different. It is used to stress the simple truth of a statement or description. 'The game just began' = the game simply began 'She just wanted to say goodbye' = She simply wanted to say goodbye. Since both tenses are possible for both meanings in American English the difference can be noted only by the context in which the statement is made.

hello... just want to ask if IS BEGUN is okay to use instead of HAS BEGUN??? and you help provide me with some explanations. thanks a lot

In this instance, there is no difference. I just did it = I've just done it.

The full form of the first one is: The game has just begun. This means that the game is currently going and just started a moment ago. You might phrase it this way if, say, a friend just showed up to watch the game with you and you want to reassure them they didn't miss too much. The second one CAN have the same meaning as the first. However, it can also have the meaning that, since the game has already begun, you are too late to join it. If I showed up to a Scrabble party, for example, and my friends had already started playing, and they said to me, "The game has just begun," I would assume (likely correctly) that I could still pull up a chair and join in. If they said, "The game just began," I would still ask them (or need to tell from their tone of voice) if I could join, or if I was too late. The second one can also mean that the event happened spontaneously, with little or no preparation. For example, if you are standing around with a bunch of guys and someone starts kicking a soccer ball around, and then you all start playing soccer, you might have a conversation like this: Someone else: I didn't know you guys were going to play soccer. You: We didn't either. The game just began! The implication being the game started itself, so to speak - it wasn't planned. They are pretty similar phrases, but the second one has more meanings depending on context and tone.