University does not explicitly request either a motivational letter or recommendation letters I am applying to University of Helsinki for Master degree, just filed the application. But the weird thing about it - they do not explicitly ask neither for letter of motivation nor recommendation letters. They only mention motivational letter very briefly on just one page, but after I filed online application their system said that I just need to provide my transcript of records and degree certificate, that's it.  

The other thing that confused me - in the online application they asked me to write brief message why I am applying to their university (under 2000 symbols). They didn't call it "motivational letter", but can it be that they take this short 2000 symbols online input form for motivational letter? I highly doubt it, but then I don't see the point of writing it, when they will have the same thing(even more detailed) provided to them in separate letter.  

As for recommendation letters - I think they don't mention it at all, at least on the main pages concerning applications for Master degree.
This is not common for Finnish university, many other universities explicitly demand recommendation and motivational letters.  

My question is - can I be sure that the admission board will read my motivational and recommendation letters? I always thought that the main thing admission board looks at are these two type of documents, am I wrong?
Finnish students are typically granted a permission to study the Bachelor's and Master's degrees both with a single application after completing upper secondary school. Therefore, there is practically no culture of writing recommendation letters before the PhD level, and even then it is kind of a rare thing.
The situation is only slightly different for foreign students, since the universities want to make sure they are recruiting good students, given that there are no tuition or other fees except the compulsory 100€ per year for almost all-inclusive dental and other health care.
In the specific page you link to, it is stated that

Admission will be based on the grade, applicability of the previous degree, the motivation letter, and the possible preliminary assignment which is used to assess the applicability of the applicant’s previous competence.
The applicant must enclose with his or her application a copy of the diploma, an official transcript of completed studies and a motivation letter describing the applicant’s personal goals and reasons for applying.

Therefore, it would appear on a first look that no recommendation letters are sought, which is what I would expect.
The comments asked for additional clarification. For example, the Faculty of Social Sciences of University Helsinki writes

Please, submit only documents required. Any additional documents like articles written by an applicant, recommendation letters etc. will not be included for evaluation of an application. If a research plan (including references) is longer than 5 pages, the extra pages will be cut out.

in their PhD application guidelines. In most cases, the system here is just very different.
Anyway: better safe than sorry. Ask them what to do.