一只给你的视频。 That line was from an author on YouTube. One commenter posted that for video it is not 一只 but 一支.
My thinking was that the author meant: A (or one) video for you only.
Question: Can that line be understood as my interpretation above? Could that be what the author meant?
When 只 is used after 一，it is always interpreted as a measure word. If you want to say "A video for you only", it will be "一段只给你的视频", or "只给你的视频".
Also the character 只 as a measure word evolves from the action of catching a bird:
Source:http://qiyuan.chaziwang.com/etymology-14538.html
Therefore it is mostly used on animals:
一只鸟 a bird
一只狗 a dog
一只老鼠 a mouse
or body part:
一只手 a hand
一只脚 a foot
Both 只 and 支 could be measure words and sometimes can be interchangeable.
e.g.
一支戒指 一只戒指
兩支光纖模組 兩只光纖模組(Optic module for network device)
From my experience, 只 is commonly used in formal documents, such as contract, quotation, etc.
For objects which is long and straight, you can only use 支 instead of 只.
e.g.
O) 後院有支很長的竹竿可以晾衣服。
X) 後院有只很長的竹竿可以晾衣服。
O) 我的筷子掉到地上了，幫我拿支乾淨的。
X) 我的筷子掉到地上了，幫我拿只乾淨的。
For songs, movies or youtube videos, you can use 支. (correct, but a little bit rare.)
e.g.
那支(首、個)動人的歌曲，是我最喜歡的歌星唱的。
你說的那支(部、個)電影，我才剛看而已。
Youtube昨天最熱門的那支(個)影片，我等一下分享給你。
只 zhi1 (traditional 隻), a classifier, is completely separate from 只 zhi3 (traditional 只), meaning "only".
一只 is the former and cannot have the meaning "for you only".
只 is not a classifier I've ever seen used for videos, so I'd guess it was either used in error or the author's use of artistic license to make the video seem "cute", like 一只猫 or 一只小鸟.
