Why are anti-dumping duties considered to be non-tariff barriers to trade?

It all comes to taxonomy. By definition of non-tariff barrier (Beghin 2016):

Non-tariff barriers (NTBs) refer to the wide range of policy interventions other than border tariffs that affect trade of goods, services and factors of production. Most taxonomies of NTBs include market-specific trade and domestic policies affecting trade in that market. Extended taxonomies include macroeconomic policies affecting trade. NTBs have gained importance as tariff levels have been reduced worldwide.

So by definition any policy that affects/limits trade that is not taxonomically tariff is a non-tariff barrier. Now when it comes to trade policy taxonomy anti-dumping duty is simply defined as a separate category from tariff (even though it might involve taxes at the border). Following Dinlersoz & Dogan (2010):

... A tariff is typically designed to maximize either domestic revenue or domestic welfare. An anti-dumping duty, on the other hand, is usually set to make up for the difference between a foreign firm's price at home and the price of its exports, provided that the latter is lower. ...

... Tariffs are usually imposed uniformly on all foreign firms exporting a given good to a domestic market. Anti-dumping duties, on the other hand, target a specific foreign firm or a group of firms which are claimed to be dumping, that is, selling at prices deemed “unfair”. The goal is to restore fair pricing, where the yardstick of fairness is usually the price prevailing in the foreign market. The tools differ also in terms of the institutional and political process they need to go through to be initiated. Furthermore, there are cases where antidumping duties are introduced in an industry already protected by tariffs. ...

Hence even though there are some similarities these policies will have their own separate categories and thus by definition anti-dumping duty is not a tariff (this is similar like in biology fox and wolf will be different categories of mammal even though they are similar animals).

Also, one question additionally, are duties based on personal preferences, e.g. political motivation, also non-tariff barriers to trade?

Depends on what sort of duty it is and what it is conditional on. If it is tax on all foreign products of certain kind (coming from a specific country) then likely it would qualify as a tariff. If it is tax that is applied only to one foreign company due to some animosity likely it would not be tariff. However, the terms can be sometimes applied loosely.