No! That is a small mount Husqvarna bar that will bolt to your 257. You see that it is a K095 bolt mount pattern? It is 24" long from the end of the mounting slot to the tip. It uses regular 3/8" pitch chain with .050" driver gauge and the chain needs 84 drive links.
If you are going to get a Jonsered 2166 you need a bar with a D009 mount. (Oregon 240RNDD009) with the loop of 3/8" X .050" gauge chain that is 84DL you already have in the picture.
A D009 X 24" bar will work perfect on your Jonsered 2166.
Yep, and no saw with a K095 mount will be really happy with a 24" bar - but some of them can of course use it in a pinch. Balance will be very front heavy - not nice to handle at all.