You can think of a hand closed around a throat. The person is still standing and still there, but no air gets through and nothing can be done. Everything the word does grows out of that one picture: whatever is held is not gone, it simply cannot act any more.
The source gives the word as strangle + hold — literally the kind of hold that strangles. The picture in the word is therefore its own history.
來源資料寫這個字由 strangle（勒住脖子）加 hold（抓法）組成，字面就是「會讓人窒息的那種抓法」。所以這個字的畫面和它的來源是同一件事。
Wiktionary entry for stranglehold, etymology: “From strangle + hold.” (packet ref kaikki:3f6f69a190036ae4:1215552132:5338)
From the picture
讓對手動不了的掌控
把脖子換成市場、產業、一場比賽或一個組織，那隻手的效果一模一樣：對方還在，但什麼都做不了。這一層是今天最常用的用法。
noun · C1
Complete control over a market, an organization, a situation or a game, so strong that other people cannot compete or act freely. It is almost always singular: a stranglehold on something.
壟斷式的掌控
noun · C1
A tight hold around someone's neck that stops them from breathing, for example in a fighting sport or when someone is held down.
鎖喉