Generally animation should be used sparingly for these purposes:

- To draw the user's attention to something that's happening but might otherwise go unnoticed
- To provide feedback about the result of a user action. As an example, animation can highlight that a message was successfully sent or that it failed.
- To illustrate to a real world situation that can serve as a metaphor for the interaction

Note that's a generic list, there are more situations where animation adds value and some cases where the situations above doesn't benefit from the use of animation. 

From your description the examples above seem like a good opportunity for animation, as they're providing feedback that's important at that moment.

The second point about "when they're gone, they're gone" illustrates a different problem. These types of animations should be used to convey when something has changed but shouldn't be the only indicator if there's value in showing the information persistently. In the case of "new life" changes there should be a way for the user to see the total number of lives they hold at the time. It may not be important to know when each life was earned (which was communicated at the time with animation) but there's value in knowing the current number of lives. I'm not a gamer but typically these sorts of counts are always visible or can be seen with minimal interaction like showing a map or some sort of overlay.

Somewhat unrelated, using animation excessively often causes users to discount their value at times when they actually communicate something important. It's necessary to be discerning when deciding to add animation. If it doesn't convey something important it's often a disservice to the user.

Thanks for caring enough about the use of animation to ask. There's a tendency to go hog wild and add animations and other eye candy just because one can, rather than using them appropriately. I think this is a great post, a better title might make it more discoverable for people with the same question.