I'm just gonna give you advice based on the first match of that video that you provided.
You need to work on your tech skill. A lot of times you would jump out of your shine, where you could of easily done a reverse waveshine/waveshine turn. Suiciding because you airdodged doesn't help the situation either.
Your edgeguarding/hogging needs work as well, mainly with reading your opponent and predicting where he is going to go. At one instance, Captain Falcon was below the stage and recovering, and you forward-smashed. Edgehog and shinespike when needed! I think there was another time where you simply tried to SHL the recovering Falcon.
In general, I just think your method of fighting a Captain Falcon on Yoshi's Story is slow and predictable. You would literally stay in one place and do repeated fullhopped bairs. I found it amusing that after the Falcon would die, you would do wavelands all over the platforms. Since Captain Falcon supposedly doesn't have much mobility on stages like YS and FoD, use that to your advantage. MOVE ALL OVER THAT STAGE, and don't stay in one place. Those wavelands will surely help you on that. Use Fox's mobility on those stages to your advantage, and don't camp the middle of the map with bairs
You're handicapping yourself by sitting there and bairing. Have some variety and use throws, i.e. don't do SHFFL'd n-airs 95% of the time. And when you do SHFFL, be sure to transition with a clean waveshine to grab! Fox can juggle CF for godly amounts of damage, especially on Yoshi's Story.
Also, when Falcon's at a high percentage, don't keep on using those n-airs! They just don't get the job done. That's when you transition to grab -> u-air, drill -> waveshine -> uthrow -> uair, or even drill -> waveshine -> upsmash. Or start predicting his movements and hit him with a well-timed upsmash when he goofs up.
That's all I can see for now. I'll probably watch the video again to give you more pointers, cause I just suck at giving you all the hints in one sitting. Main point of the post:
Don't do repeated b-airs, as your mobility alone on a stage like YS and FoD pressures a Captain Falcon.