The importance of attributes comes directly from the computer RPG's origin as a representation of tabletop RPG combat systems. Wizardry, the game which really kicked off the genre, was mostly Dungeons & Dragons with the serial numbers filed off. By the late 1980s, Advanced Dungeons & Dragons games officially translated the tabletop rulesets to the screen. Creating a character was known as "rolling" because you threw the dice to discover his or her inherent Strength, Agility, Charisma, etc. In D&D, those statistics were largely permanent, defining the character through the entire game or campaign. Some video games, like Ultima, took advantage of the malleability of the medium to allow attribute increases. But apart from spells, attributes tended to be the bulk of character customization in terms of mechanics.
But computers and consoles can process information faster than a dungeon master with a set of dice, so more complicated statistics were introduced. Wizardry VI and Wizardry VII introduced a complex system, balancing permanent character race with dynamic class and attributes, using dozens of different skills as the primary mechanism for character progression. Other games in the early 1990s followed suit: Betrayal At Krondor made skills far more prominent than attributes (which only included Speed and Strength anyway). The Elder Scrolls: Arena, first in that series, used both skills and attributes.