This video shows how to make an animated texture - similar to the one demonstrated in my lecture. This one is a shrinking crack. Ideally it would be a growing crack, I just didn't change the names of the textures around.

Alternatively, if you couldn't be bothered watching a 5 minute video, to achieve an animated texture do the following:

Create a series of CryTiffs with the same name with a number that increase by 1 ie Texture01, Texture02, Texture03

Have them all located in the same folder - ideally within Game>Textures

Copy one of these CryTiff and rename it something similar to this
Texture##01_03(0.5)
Where Texture is the common name you used
## is the number of digits ie a sequence to 100 would be 001, 002, ..., 099, 100 so would have 3 hashes
01_03 is the range of textures you want to sequence through in the animation
(0.5) is the amount of time in seconds you wish to stay on each texture during the animation

Assign the Texture##01_03(0.5) or similar as to the diffuse slot of the material within CryEngine

The video tutorial goes into more detail if in doubt. It also briefly covers how to create a material from scratch within CryEngine to assign to an object. Useful if you are still getting the Replace Me texture on imported objects - but it's much better to fix that problem within Max - use as a last resort