とりあえず is used when you do/say something easily done/said before getting to a main difficult part.
- 仕事の前にとりあえずコーヒーを飲んだ。
Before my work, I had a cup of coffee first.
- 説明は難しいですが、とりあえず間違っているとは思います。
It's hard to explain, but I think it's incorrect anyway.
- 何を見るかはともかく、とりあえず映画館に行こう。
Putting aside what to watch, let's go to the theater first.
- とりあえずでやったことです。
I did it as a quick fix.
- とりあえず、安心しました。
At least, (I can say this now,) I'm relieved.
The use of とりあえず in your video is tricky and atypical, but it comes off to me as "it's not a big deal (to me)" or "I experience this very commonly", as if "its falling" were something he(?) experiences thinking とりあえず. It explains the following exchange, too:
岡崎さんはその、たまに取れるんですか!?
So it... falls every now and then?
と、とりあえず。
とりあえずって!? そんな簡単に取れてしまうものなんですか!?
"Toriaezu", you say?! It falls off that easily?!
"I guess" is certainly not a dictionary translation, but I cannot think of a better translation...