How SM ensures that the items discussed in Retrospective meeting are followed

For who are these improvements? Who expect to benefit from them?

During the Retrospective, did the team consider whether improvement items ought to be small, measurable, achievable, realistic, and time-bound? Did they receive this or any other guidance in the matter of actionability and validation?

The short answer is to make them visible.

The Scrum Guide says this:

The Sprint Backlog makes visible all the work that the Development Team identifies as necessary to meet the Sprint Goal. To ensure continuous improvement, it includes at least one high priority process improvement identified in the previous Retrospective meeting.

Personally, I keep a backlog of improvements from all of the Scrum Teams, classifying them as "Impediments" (referring to something that obstructed or hindered the team) or "Improvement Opportunities" (ideas that people had that may make things better). I keep track of what team(s) reported each issue and keep them in a backlog or a Kanban board that is visible, ordered, reviewed, and updated on a regular basis and I tend to work on items on these boards with the right stakeholders to progress them to resolution. Teams also use their Sprint Backlogs as suggested in the Scrum Guide to track improvements or parts of these improvements that they are responsible for.

Outcome or the most important improvement decided by the team goes into sprint backlog. 

One tip I do as a Scrum Master facilitating the Sprint Retrospective: early in this meeting I bring up the list of the action or improvement items the Development Team decided to work on this current Sprint. I have them vote as a team on a scale of 1 to 10 as to how they feel they did for each one. This leads to a discussion, especially if someone votes 3 and someone else votes 10, as an example. This helps with transparency, and if improvements are not getting taken care of, then the team has some data to inspect and adapt.