The definition you provided of robbery in Alabama is the definition of robbery in the first degree and appears to be most relevant here. The required intent for that charge is the intent to commit a theft. If you intend to commit a theft and cause injury (whether you intended to do so or not), it is robbery in the first degree.
To commit an assault in Alabama (AL apparently defines assault as most jurisdictions define "battery" and calls "menacing" what most jurisdictions call "assault"), the person who causes the injury must have *intended* to cause injury. Such an intent is not required for a robbery charge.
For assault to be a lesser included offense of robbery, robbery would have to require proof of each element required for assault and then more (i.e. the following would have to be true: if you committed a robbery, you *necessarily* committed assault). For example, if assault required A and B, and robbery required A, B, and C, assault would be a lesser included offense of robbery. But that is not true here. Robbery does not require proof of each element of assault, because it does not require intent to injure. Thus, one can commit robbery in the first degree without committing assault. For that reason, these individuals could be charged with both crimes.