If the Drengin had range boosts to the lasers and YOU had range boosts to your missiles it is entirely like that the Drengin DID fire first since laser are much faster and with range boosts can in fact get in about the same range as missiles.
The components which boost range are:
The Bane, very late-game, boosts the range of all three weapon types by 50%, one per ship and affects every ship in the fleet in which the ship mounting the Band is found.
The Energy Accelerator, relatively early game, boosts the range of beam weapons by 30%, one per ship and affects only the ship upon which it is mounted, costs elerium.
The Slingshot Booster, relatively early game (similar position in tech tree to Energy Accelerator), boosts the range of missile weapons by 25%, one per ship and affects only the ship upon which it is mounted, costs antimatter.
The Kinetic Accelerator, relatively early game (similar position in the tech tree to Energy Accelerator), boosts the range of guns by 50%, one per ship and affects only the ship upon which it is mounted, costs durantium.
The Acceleration Field, relatively late game, boosts the range of guns by 25%, one per ship and affects the fleet in which the ship upon which it is mounted is found, costs Durantium.
So, under the assumption that only one of each fleet-wide range-boosting module is in effect per fleet, the attainable end-game range boosts are 75% for missiles, 80% for beams, and 125% for guns. Basic weapon ranges are 1100 for missiles, 800 for beams, and 600 for guns. End-game weapon ranges are therefore 1925 for missiles, 1440 for beams, and 1350 for guns. Yes, range-boosted beams quite obviously have similar range to range-boosted missiles by the end of the game. Oh, wait, no, the relative range advantage held by missiles hasn't actually changed that much (at base range, missiles have 37.5% more range than beams; at the above end-game ranges, the missiles have 33.7% more range).
What if we remove The Bane from the picture and only look at the standard range-boosting components, under the assumption of no more than one fleet-wide booster per fleet? Well, in that case, the attainable weapon ranges are 1375 for missiles, 1040 for beams, and 1050 for guns. Hmm, the relative range advantage held by missiles when both the missile and the beam ships have range boosters still hasn't changed that much (the missiles have ~32.2% more range than the beams).
Thus, under the assumption that both sides had similarly advanced range-boosters in play, it is in fact nonsensical to claim that beams or guns have 'about' the same range as missiles. It is still theoretically possible for the ships which mount beams or guns to get the first strike because missiles are slow-moving (though I'm not all that certain that the simulation doesn't just apply the damage when the weapon is fired rather than waiting until the projectile reaches the target to apply damage; what with the other inaccuracies seen within the battle viewer it wouldn't surprise me if projectile speeds have no effect on anything but visuals), but under the assumption that the rate of closure is about 80 between the time missiles come into range and the time beams come into range, that's not terribly likely; the absolute range difference between missiles and beams is not less than 300, and at a rate of closure of 80 range/s that means that missiles will be in range at least 3.75 seconds before beams are (if boosted to the maximum ranges given above, the range differential is 485 range units and the time taken to close the game is 6.0625 seconds at a rate of closure of 80), and most missiles other than the very earliest will be able to hit their targets from maximum range before beam ships close to firing range (for example, Harpoons and later missiles can hit from 1925 or 1375 range before beams come into range to fire on the missile ships while Stingers and later missiles can hit gun-armed ships from 1375 range before gun-armed ships can land their shots though not before the gun-armed ships can fire if gun range is boosted to 1050, assuming the weapon speed numbers given in the game files are accurate and matter to the simulation and that the rate of closure between the opposing ships is about 80 range per second).