Using a combination of spatial and non-spatial inputs for convolutional neural networks
Yes.  One way is to start with several convolutional layers, and then end with one or two fully connected layers.  You can add the other features as inputs to the first of those fully connected layers.  This is basically serial composition of convolutional layers then fully connected layers.

There are other options for network architectures, but that'd be a reasonable one to try first.  The choice of architecture is an art and depends partly on how you think one might learn from the features, and how the value of one feature might affect the kinds of things you'd like for in other features.  The architecture I suggest above would be good if we pretty much want to look for the same kinds of information about the pixel input, regardless of the value of health, ammo, etc.  If you think the health, ammo, etc. would dramatically influence what kinds of information we'd want the network to extract from the pixel input, one might consider other network architectures.