The inlcusion of arquebusiers and cannon in Chainmail seems unusual coming to the rules from Dungeons & Dragons, especially given the long-time exclusion of gunpowder weapons from D&D. They are also striking in a historical sense, as the inclusion of gunpowder weapons on the battlefield in Europe generally heralded the change from older medieval tactics and organizations to pike-and-shot and other characteristically Renaissance-era formations and tactics. Their inclusion here allows for some play in the transition, especially the Hundred Years War and the Wars of the Roses. They also allow experimentation with Chinese historical armies where guns were included earlier and wielded more frequently.
In game terms, arquebusiers are similar to heavy crossbowmen as far as movement, rate of fire, fire arc and the prohibition against indirect fire. So arquebusiers can move up to half their regular move and either fire or reload. If they make more than a half move, they must beat their opponent's die roll to fire and may not reload. They fire every other turn.
Where arquebusiers are completely different is in the way that their hits are resolved. Archers and crossbowmen are required to be grouped, and their effectiveness depends on the number of models in the group and their targets' armor. For arquebusiers, you roll a die for each gunner model. The range to the target determines how difficult it is to hit. All hits kill their target, regardless of armor!
Hard cover that conceals more than half the target imposes a -1 penalty on the roll to hit. If more than half the target is covered, the shooter has a -2 penalty. These penalties are partially offset if the shooter is using a rest or mount. If the shooter is using a support, they receive a +1 bonus.
Looking at these rules, arquebusiers suffer from a lack of mobility, but that is more than made up for with their effectiveness shooting. They have the potential to easily dominate the area of the battlefield within their range, especially if they are firing from a position where the guns have supports.