Where does the site display a list of games I have purchased?

account.blizzard .com/games - “Game Accounts” (russian - “Учетные записи игр”) and “Starter Editions & Public Test Regions” (“Стартовая версия и тестовый игровой мир”) only. The first, as I understand it, is an analogue of the Steam Cloud - that is, the presence of a set of personal data already tied to the game.

Where is the list of purchased games and active subscriptions?

It should be right there under /games. I checked mine and it has:

Game Accounts

  • WoW (Name) - and the option to click a link in that data line to review my subscription/game time.
  • WoW 1 - PTR
  • WoW 8 - PTR
  • WoW 8 - PTR
  • Diablo 3 RoS
  • Hearthstone (free game)
  • Heroes of the Storm (free game)
  • Overwatch (which is free to play right now but I was in Alpha and Beta)
  • Starcraft II (free now)
  • Destiny 2 (was free at 2018 Blizzcon)

Below that is the next set of games titled Starter Editions & Public Test Regions

  • It gives me the option to create a free WoW account and the option to create another WoW PTR (mine are actually Betas but not labeled right).

Next is Classic Games

  • Diablo II
  • Diablo II LOD

Missing are my Starcraft and Starcraft BW.

Make sure you are on the right Battlenet account that has your games. Also, there have been bugs in the past where game keys you have are not recognized. Sometimes a password change kicks the system and forces a data flagging reset. Other times Billing has to get involved.