I actually found the pilot video to be more humorous than the one up above. The first video you posted took itself far too seriously, and the 'jokes' when they did happen weren't all that well timed or written to begin with (I will admit, "MY SWORD HAS WEIGHT NOW!" got a chuckle)
Taaj seems to me (at least from the pilot) the one who breaks the 4th wall and at least has an idea it's a game. The others seem to be heavy caricatures of different JRPG tropes and characters.
One thing that might help is to play it up a bit. For me, the problem was they were actually too subtle in their parody, that they seemed more like actual characters you'd find in a JRPG.
Like the narrator/voice from the void. It seemed like you were getting close to having him be funny, but every time he backed off and it just seemed more like a regular JRPG. I personally would have had him be a bit more long in the tooth, maybe even interrupting Taaj as he calls him on some BS
VOICE: You are the chosen one, destined to save all the realms from certain destruction, that only you have been born to stop! Choose your class!
Taaj: Why is there a floating box next to me?!
VOICE: Excellent! You have chosen LANCER.
Taaj: No I did no-
VOICE: Welcome, mighty Lancer!
Something along those lines.