What is the logic behind definition of 1-year master programs in UK?
The article you link to lists 3 cons to a 1 year program: not enough time to take electives, not enough time for a work placement, and not enough time to get good letters of recommendation. It also lists duration, and the decreased costs, as the major benefit. The cons, however, are not particularly important in the UK (and many parts of the world) while the pro is important worldwide.

Electives:

The UK educational, and employment, system does value electives. Students start specializing at age 16 when they take their A levels. Undergraduate programs typically have no "general education" type requirements. Many MSc programs are so specialized that there are not enough electives offered to fill a second year.

Work Placement:

In the UK, work placement opportunities are not limited to students. In fact, in my field, work placements are only available to graduates and students cannot do a work placement.

Recommendations

Letters of recommendation are just not that important in the UK. For example, for permanent academic positions, letters of reference are not part of the decision process until the very end. Many jobs do not require any references at all.

Duration

For self-funded programs, a 1 year program saves you money. Even with funding, there are still opportunity costs associated with the 2nd year.

To get to your questions:


  Why don't UK universities manage their master programs in 2-year periods, instead of current short 1-year ones?


In general, as with most things, finances rule the day. While 2-year programs would theoretically bring in more money to a school, the fear is that a 2-year program would not meet the needs of UK students and student numbers would drop. This would result in decreased revenue for the school/department.


  What motivations could convince a typical international student to prefer a 1-year master program at UK to a 2-year one at north america?


My UK school pitched our MSc program to US students as: if you know what you want to study, why waste money and time studying other things