Solved it myself.

There are fields Global: Contextual Links and Content: Edit Link, so you enable both, set Content: Edit Link as Exclude from display and in Global: Contextual Links settings select the fields you want to be included inside contextual links, so in this case the Content: Edit Link.

However this works correctly and fine only while in preview mode, when watching the actual page in action the links nor the cog icon does not appear. As I understand this is some kind of a bug.

To fix that, you need to add additional CSS to your theme, which is (in my case):

.views-field-contextual-links {
  position: relative;
}

And now everything works fine, every element has it's own drop down cog/link.

Solved it myself.

Steps:

1. Enable Global: Contextual Links and Content: Edit Link fields
2. Exclude Content: Edit Link from display
3. In Global: Contextual Links settings, select the Content: Edit Link

However this works correctly and fine only while in preview mode, when watching the actual page in action the links nor the cog icon does not appear. As I understand this is some kind of a bug.

To fix that, you need to add additional CSS to your theme, which is (in my case):

.views-field-contextual-links {
  position: relative;
}

And now everything works fine, every element has it's own drop down cog/link.

Solved it myself.

There are fields Global: Conditional Links and Content: Edit Link, so you enable both, set Content: Edit Link as Exclude from display and in Global: Conditional Links settings select the fields you want to be included inside conditional links, so in this case the Content: Edit Link.

However this works correctly and fine only while in preview mode, when watching the actual page in action the links nor the cog icon does not appear. As I understand this is some kind of a bug.

To fix that, you need to add additional CSS to your theme, which is (in my case):

.views-field-contextual-links {
  position: relative;
}

And now everything works fine, every element has it's own drop down cog/link.

Solved it myself.

There are fields Global: Contextual Links and Content: Edit Link, so you enable both, set Content: Edit Link as Exclude from display and in Global: Contextual Links settings select the fields you want to be included inside contextual links, so in this case the Content: Edit Link.

However this works correctly and fine only while in preview mode, when watching the actual page in action the links nor the cog icon does not appear. As I understand this is some kind of a bug.

To fix that, you need to add additional CSS to your theme, which is (in my case):

.views-field-contextual-links {
  position: relative;
}

And now everything works fine, every element has it's own drop down cog/link.