Does this mean if I were to, for example, research straight through the line of techs to get Laser II in one match the cost of the Laser II tech would be cheaper than if I were to, in another match, research many other techs in addition to the line of techs required to get to Laser II?
Yes. The more techs you research, the more expensive all future techs will become. Weapon-techs are especially affected by this cost-inflation.