I often watch my children play cards is the better way to say it. Playing (present participle) is for an action happening right now, at this moment. If you were, at this moment, watching your children playing cards, you would say, "I am watching my children playing cards". It would describe what you are currently doing.

Sentences with verbs of perception ( see, watch, listen) can be followed by either a gerund ( playing) or a bare infinitive (play). In many cases, the meaning is the same. There is a difference, however. If you use the infinitive, it means that you observed the whole process; if you use the gerund, it suggests that you only saw part of it. Here's an example: Imagine that someone wanted to find out who had eaten all the chocolates that were in a box. You might say: "It might have been Mary. I saw her eating them." This means that you observed Mary while she was in the process of eating chocolates. Perhaps you walked through a room and caught sight of her with her hands in the box and a chocolate or two in her mouth. or "I know it was Mary. I saw her eat them." This means that you saw her eat the entire box of chocolates. In your example of the children playing cards, you could use either construction. The verb 'watch' suggests that you watch entire games. So both are equally correct and have the same meaning. Note that the phrase 'that's fun' can't just be tacked on the end with a comma before it. You either need to connect it with a conjunction ( "I often watch my children playing cards because it's fun") or put a full stop and add it as a separate sentence.