He looks comfortable and happy to me, maybe just wanting someone to interact with. At 0:20, that's a contact call. They use it to call out to other birds. He is probably not used to being the only bird yet, and I think a lot of his body language was a reaction to the sound from the kid in the background.
My budgie bonded to me after his mate died, so when he does his "contact call" it's usually because he misses me or needs something (although sometimes he's calling out to native birds....or running water). I usually respond with a specific whistle. Then he'll call back in response, and we'll go back and forth. If at all possible I go see him when he calls to me though (I don't want him to get depressed from loneliness, as they are very social creatures). I will give him a kiss and/or talk to him for a bit, and he'll be satisfied. He also uses his call in the morning if I haven't opened the blinds or given him his bowl of fresh food yet. He doesn't let me forget! But I can differentiate based on context and body language.
You seem really in tune to your budgie, so I think you will learn his sounds and body language soon enough! He will also learn YOUR body language, habits, and sounds, and that will help communication as well.