Why did he say "it"? Can I skip it?

Does the phrase "game day" only refers to sports?

Generally, yes! "Game day" isn't used for anything other than sports, the day of official competitions in sports. Even if someone is playing games the whole day, you probably wouldn't call it "game day." Ex: It's the big game day this weekend! Are you coming to watch it? Ex: I'm going to paint my face in the team colors on game day.

What does "allegiance" mean? In what circumstances could I use it?

"Allegiance" means loyalty, commitment, and faithfulness to something or someone, usually a superiority. It's quite a formal word and is usually used to show your thorough commitment to a person or organization. Such as a king, a nation, a government, a party, or a side of something. It's also common to hear it in series and movies where old English is used or in battlefields. Ex: I swore my allegiance to my nation, and I'll protect it at any cost. Ex: Where does your allegiance lie? With us or with them?

Could you explain me about the expression "big time"?

"Big time" is an informal expression used to mean "successful," "important," or "to a high degree." In this video, "big time" means "important". For example, if someone says they messed up something "big time," it means they made a huge mistake. If someone says that someone is a "big time politician," it means that they are a very successful politician. Ex: Rosa from my fifth-grade math class is now a big-time celebrity. Ex: I messed up my interview big time. I don't think they're gonna give me the job.

What's "caught up" mean?

To be "caught up" in something means to be involved in a situation involuntarily. It can also mean giving too much of your attention to something, or it can mean that you've shared recent updates with someone and "caught them up" with what's going on. Ex: I caught up with Jane this weekend over coffee. Ex: I got so caught up in the situation that I forgot to ask how you were doing. Ex: Don't get caught up in any drama.

What does "by the way" mean?

"By the way" here is used to make someone aware of some extra information, or to talk about something you just thought of. It is similar to the word "additionally." Ex: By the way, I'm allergic to fish. Ex: Oh, by the way, I have a funny story about that.