Not necessarily. Assuming equal ability modifiers and same weapons (long sword in this case), you could build an assassin striker to be the following. If you assume the assassin could get a surprise attack in a combat encounter the same number of times a fighter can action surge, the numbers would look like this:
Rogue 1: Dmg 1d8 longsword + 3 Ability Mod + 1d6 sneak attack = 11 average damage per round
Fighter 1: Dmg 1d8 longsword +3 ability Mod = 7.5 damage per round
Rogue 5 (assassin): Surprise round = (1d8 dmg +3d6 sneak attack)*2 (assassin) +4 ability mod = 34 points of damage. Every other round is 1d8 +4 +3d6 = 19 points per round
Figher 5: Action surge round: 4 attacks each at 1d8+4 dmg = 32.5 points. Every other round is 2d8+8 (2 attacks) = 17 points per round
Rogue 11 (assassin): Surprise round = (1d8 +6d6)*2 (crit hit) +5 = 56 points. Every other round is 1d8+5+6d6 = 30.5 points
Fighter 11: action surge: 6 attacks at 1d8+5 = 62 points of damage. Every other round is 3 attacks at 1d8+5 = 28.5 points.
*Edit* In my actual play experience, the assassin actually gets the drop on opponents (surprise) more often than once per short rest, which is how often the fighter above gets action surge. And with the rules for sneak attack work, an assassin worth his or her merit will be able to apply sneak attack damage to just about every attack. So if your criteria for a striker is to do more damage than other martial classes on a consistent and reliable basis, the 5e assassin rogue fits that role.
DPR designed 5E fighters do not use 1D8 weapons. They use two handed weapons or two weapon.
Plus, you gave the rogue the assassin subclass without giving the fighter a subclass. A (non-variant human, i.e. most fighters) battle master using the Great Weapon Master feat and Feinting Attack does at level 5, Nova round (i.e. action surge plus Feinting Attack): 1 attack at 2d6 (reroll 1s and 2s) +d8 +13 dmg plus 3 attacks at 2d6 (reroll 1s and 2s) +3 dmg = 59.8 points. Every other round is 4d6 (reroll 1s and 2s) +6 (2 attacks) = 20 points per round. The fighter also has 3 other feinting attacks that he can manage between short rests (which have advantage and do D8 more damage) which he can use for mini-nova rounds that do 1 attack at 2d6 (reroll 1s and 2s) +d8 +13 dmg plus 1 attack at 2d6 (reroll 1s and 2s) +3 dmg = 37.2 points. The battle masters mini-nova rounds average more damage than the assassin's nova surprise round.
And every critical and every foe dropped with the two handed weapon gives the fighter an extra attack. Plus the fighter controls when he novas, the assassin is limited to when he gets a surprise round, so the DM controls a lot of that (and nothing prevents the fighter from being able to stealth and get attacks in surprise rounds just like the assassin, just maybe not as often).
Also, fighters get more attacks per round starting at level 5. Hence, +1 and stronger bonus weapons add their bonuses to every attack, not just one per turn. As does magical buffs from spells and items. The party buffer would be better off buffing a 5th or higher level battle master more often than a 5th or higher level assassin.
Note: your rogue damage should also take into account a second weapon as well, especially since it helps with getting sneak attack damage in, even if the rogue misses with the first attack.
Put together any 5E rogue you want to. He will probably not average more damage than this fighter and I did not even try hard to optimize this guy. Just gave him one feat, one two handed weapon, and one maneuver.
Your damage assumptions are flawed. You should be using DPR instead of damage because DPR takes into account criticals and misses which matter for both the rogue and fighter. Many of the DPR leaders on the optimization boards are fighters. I have yet to see a Rogue DPR leader.
Can DPR rogues be close behind DPR fighters in overall damage? Sure. There might even be levels or certain combos where the rogue wins out. But, if a DPR rogue is a striker, a DPR fighter is a striker too.
