Q:

Does the streak mechanic still offer rewards?

In splatoon 1, there was a streak mechanic, where after a few games, your streak would go up, and you could cash in your streak once per day by talking to the cat right outside the tower.
The streak indicator is still there in Splatoon 2, but talking to the cat now just gives you random trivia.
Is there still a way to 'cash in' your streak?

A:

According to kellylc on Reddit:

You get a freshness bonus instead now when you fill up the meter
  that's under where it says dry/raw/fresh/SUPERFRESH!

So you should receive your rewards automatically without needing to cash them in.

