As a Remy player myself, I can tell you that a good Remy (which your opponent wasn’t) will want to get you into the corner because that’s where Remy’s possibilities really open up combo/damage wise.So don’t get cornered.
Learning to parry the LoV’s is definitely a must, but if it were me, I’d almost WANT you to parry them because while you’re stuck in parry stun, I’m busy setting something else up that’ll probably hit you that WOULDN’T have hit you had you blocked it. Learning to parry is very important, but parrying is just like attacking. You don’t want to just blindly parry everything, you have to consider the situation. Sometimes it makes more sense to block.
In this video though, you could have parried them all and your opponent wouldn’t have been able to do anything about it. Remy is like a doll made out of matchsticks compared to Ryu. He doesn’t take damage too well and his stun gauge is short so if you can get in close, use high/low mixups he’ll be on his back before you know it. When someone’s being turtely, I’ll sometimes use a super jump to get in (they never seem to expect it) and either throw or combo them from there.