Generally speaking you can shoot arrow on both sides of the bow. With three fingers (mediterranean) most people people prefer to shoot on the left side (assuming they are drawing with right hand) and without khratra (I like shooting with khatra on the left side actually, but I am weird like that). Without khatra you hopefully have roughly correct spine of arrows, otherwise they might go to one of the sides. However you can shoot on the left side though it requires bit more dexterity or form adjustment.
Thumb draw and slavic draw are generally used on right side of the bow, these drawing styles are more "stable" during movement (for example while on horseback or while running arround) because they push the arrow to the bow a little bit. Thumb draw is also roughly 2 inches longer than finger draws (three finger and slavic) when same arm / shoulder position is achieved, so "bit stronger". Right side drawing styles tend to use khatra to deal with incorrect spine and to add bit of speed to the arrow (assuming you are using lightweight short limbed "horse bow"). However you can use thumb draw on the left side but you will loose most of its advanages such as increased stability while mobile.
In general, reloading from the right side is faster, but to be honest this is mainly relevant for speed-shooting, which is effectivelly applicable to a bow that feels light to you - which means that you are trading few powerful shots for many weaker shots. Also you can shoot very fast from the right side as well - kassai rapid fire style (possibly used by Huns, Hungarians and other steppe cultures that were using relatively "large" horse bows). Very small bows at medium to high draw weight can be effectivelly shot only with thumb ring - for example turkish bows.
Left side shooting in the movies is mostly derived from modern olympic archery, which is based on Victorian era archery not on the hundred years war longbow archery or lets say byzantine "horsebow" archery. Arguably majority of Europe was actually using "horse bows" - Slavs, Byzantines (Romans), Italians, perhaps Spaniards and Portugese, obviously majority of Arabs and Turks living in Europe, all the other steppe people such as Hungarians, Avars, Tatars, etc. Longbows very generally used in areas that were not very favorable to composite recurve bows (horse bows / asiatic bows) or when you wanted to equip armies with bows cheaply and fast. Notably Welsh, English, French, pre-turkic Arabs, Numudians / Abyssians and Vietnamese are famous for using long bows. Chinese possibly used them too to some degree, at least in "peasant" armies. Honarable mention goes to Japanese who used laminated long bows from horseback and on foot (Yumi).
If you want to shoot from right side with this "three-finger-method" you need to use slavic draw => your index finger must be straight pressing on arrow body. The way this clown is shooting would just lead for arrow to fall off. + that ridiculous handguard 
. So cool
