As the title says, is blizzard tracking my ingame-playtime for hearthstone like steam does?
If yes, where can I find this?
If no, is there a good way to estimate that number? E.g. is there a statistic for the average length of a game?
No, there is no such builtin statistic.
However, you can get a rough estimation. If you click on the quest tab ingame you can see your total play mode and arena wins. Sum those numbers, double the result and you get your total number of games played (assuming a 50% winrate).
The average game length is around 5 to 10 minutes, depending on you personal style. If you play a lot of aggressive decks then it's shorter, if you play a lot of control decks it's longer. Now you can roughly calculate your game time. Note that this does not include other gamemodes like brawl or adventures. But it's all you can get.
Obviously there are many unkonwn factors, so this method can never give accurate results. It rather gives you an idea of the magnitude of your time spent in game. You could however track your game times over like 100-200 games to get an accurate value to use in above calculation.