Not every winning attack is a string of checks. Sometimes the strongest move is quiet: it gives no check, but it creates a threat of mate that nothing can stop. That is hisshi 必至, brinkmate.
Once you have given hisshi, your opponent has one move left. If they can't mate you with it (or keep checking you), you win.
Check it yourself: the gold on b7 already covers a8 and b8, so Gote's only legal move is the king to b9 — and then G*b8, supported by the gold on b7, is mate. (The lesson checker tries every defence against the engine.)
Hisshi versus tsumero
A tsumero 詰めろ is a threat of mate the opponent can still parry. Hisshi is one they can't. Endgames are often a race: each side makes tsumero after tsumero, and the first to reach hisshi — while their own king is safe from checks — wins.
Speed
A hisshi is often shorter than a mate. If you can see a five-move mate but also a two-move hisshi, and your king is safe, the hisshi may be the faster win. The first question is always: can my opponent check me?