There is no second intensity pin, rather 6 pins used for color - 2 each for R, G, and B (so no intensity signal at all, in fact).
R, G, and B plus two intensity pins would give you only 32 colors (2^5), which would look quite different besides.
Yep, 16 simultaneous colors, but in The "enhanced" EGA modes those 16 are selected out of 64 possible colors. The VGA version also supports 16 colors (out of 2^(6*3)=256K colors).
I don't know of any way for an EGA card do display 64
simultaneous colors in any mode (there aren't enough bitplanes).
The second one looks like it has
less colors than the first (compare the "banding" on the arm, and on the left side of the helicopter)... also, those colors all look like they belong in the standard RGBI palette. Is that on an IBM EGA?
If so, my semi-educated guess is that the game is
trying to send 6-bit values to the palette registers, but only 4 bits are used -- that's what the IBM EGA is known to do in 200-line mode. This produces a different palette compared to the "standard" EGA shot, but colors are quantized to RGBI values so it is definitely not as intended.
I don't have the hardware to test such code, but your photos actually increase my confidence that my conjecture is correct - both games show 16 out of 64 colors on "extended" EGA, and plain old 16 RGBI colors (just not the correct ones) on a standard IBM EGA.
The first shot again does not look like it has more than 16 (simultaneous) colors. At least, it looks quite similar to
this VGA screenshot, and that one is definitely 16 colors (you can verify that in software).
About the second shot, it's hard to tell because the photo came out kind of greenish, but I'm fairly confident that the colors here are RGBI ones. Which points to the same symptom as Rambo III on the IBM card: the game reprograms the palette using 6-bit values, but only 4 are actually used.