No such thing as real sci-fi - unless you misunderstand what "fiction" means ,)
I could just as easily employ the same pedantry and accuse you of intentional misunderstanding of the usage of the word 'real' in that phrase... but I think we both know what we're talking about, so I'll try to refrain.
And of course you could catch the other guy. Employ a higher acceleration than him. Or at least employ projectiles with a higher velocity. And there's no information delay, unless we're talking about combat that is occurring while both ships are traveling at near light speed, and also with an appreciable distance separating them. That's an entirely different kind of combat, but it can still be very entertaining, just look at some of the works in Alastair Reynold's Revelation Space series. I haven't really thought about putting that sort of system into a playable game, but I'm sure some clever developer could puzzle it out. Fire your main cannons (probably employing shells with autonomous semi-intelligent guidance systems in case your target shimmies to the side), go into suspended animation while you wait for it to cross the intervening light years, wake back up as soon as it was about to hit (or as soon as the light from the hit reaches you, which the smart boys say is the same 'time' ... I know when I'm out of my depth, and special relativity is one of those places for sure). I know I'd play it.
And back on the more local frame of reference, sure, you wouldn't build manned ships for space combat specifically. But come on, who do you think those drones would be firing at? Other drones? Just for fun? If there are people traveling through space, and someone wants to stop them, they may employ those drones, sure. But you still have a ship full of squishy humans to get from point alpha to point zeta. Do you think maybe they'd want to be armed, just in case?
And re: human jelly, we have shock absorbing technology now. Just extrapolate until it's sufficiently advanced. Yes, I know that's stretching the bounds of hard sci-fi a bit, but it's one thing to take an existing idea, no matter how crude, and imagine it could outgrow its boundaries, and another to imagine something that works entirely counter to hard laws of physics. (Yes, I know you can squeeze in enough technobabble to make anything seem plausible, but space buggies are never going to turn by banking against the force of vacuum. Unless you replace it with ether, which isn't highly likely to happen in this universe)
And the B5 (human) ships weren't maneuvering in such a way as to turn their pilots into jello. You can spin 180 degrees in a ship that's going at any speed without doing any damage to the pilot. It's not like they're stopping. Their velocity continues in the same direction, they're just facing backwards. Not even the barest perceptible discomfort in that. You can sit in an office chair and spin without being squished to jelly, and do you have any idea how fast the Earth is spinning, while also orbiting the sun? Spin any way you want. But let's hope Earth doesn't slam on her brakes. The White Stars, et al, were employing Vorlon technology, so of course they ran on magic. That's why I called it 'sufficiently advanced technology'. Google Clarke's Third Law if that doesn't seem to make any sense.
Also Forever War was such a great book, and I wish he'd quit while he was ahead. Anything that followed that just failed pretty hard by comparison. One of these days I'll get around to reading something Haldeman wrote that wasn't a Forever ____ book, but I'm still stinging with the letdown of those sequels so much that I'm not sure I want to let myself in for that kind of punishment again.
That went on a lot longer than I had intended. Oops.