Hey how ironic, I was at my friends house and he had the xanadu stream on and i saw DK so I started watching intensely lol. That's a good thing, cause i can give you some player specific tips. I don't think you lost due to anything meta knight specific, except for one thing which i'll mention at the end cause i want to start with the more important stuff. You actually played that matchup VERY well as far as character-vs-character.
There were a few very simple, but frequent mistakes you were making in neutral that cost you the set. Here they are in no particular order.
First, you were very unsafe with your landings whenever you jumped. If you were spacing aerials in neutral, or any situation for that matter, you would often land a few character lengths away and since meta knight is so fast, that's an easy punish/grab. I saw this happen multiple times so it would make a big difference if you avoided landing near him so... obviously. for lack of a better word.
Second, a couple times you were a little late with your punishes in the opposite situation than the one above. If he landed near you, you would wait for his aerial to end then try to run in and grab, but he just f tilted you out of it or something. Right when u see him short hop in your direction, run with a quick shffl nair and by the time your nair comes out, his aerial will be ending and he will still be in endlag when u hit him so he can't do anything
Third, you had a double jump habit which meta knight is AMAZING at punishing. Your double jump habit was usually in the situation after you get hit to the side at low-mid percent, and then got out of hitstun. You would often double jump toward him and at this point meta knight can either dash back, then run in and punish the landing with a grab due to his speed, or he can instantly punish the jump by going where you never want him to be: directly under you and spamming up airs. He did both of these punish options to you in the set.
Lastly, and this would be the absolute icing on the cake for you to beat that guy, or other meta knights in general, is you have no reason to not charge your punch when you respawn, and simply in general. DK has a free full hop cargo up throw to double jump donkey punch kill combo on metaknight, and it's honestly probably the best meta knight kill combo in the game cause it's 100% guaranteed if u don't have an input error or something silly like that. Therefore, you should pretty much always have the punch charged in that matchup. Also, keep in mind the % where it works is around the 50% to low 70s. Lower than that likely won't kill, and any higher will be harder to land the punch and at that point a fair is easier anyway.
Do those 4 things and you're guaranteed to beat that meta knight next week! good luck!
This stuff can apply to any character, minus the last part regarding the combo so hopefully it will improve your overall DK play