UPDATE:
I could not get the stock CSV product import function to work in a way that it would update the price in a reliable way in both ps_product and ps_product_shop tables.
Maybe it is because of the PHP 7.1 I'm forced to use.
I tried many things: identifying products by ID, importing more fields, various tests with different values in the field "ID / name of shop", importing duplicate rows for products in both shops (with different shop ID in "ID / name of shop" field) and so on...
Nothing works in a reliable way. Most obvious error: products with shop ID 2 are changed only in ps_product and the db field "id_shop_default" get's overwritten with ID 1...
To solve my problems, I'm lucky that the following free import/price update module does exactly as promised and even updates all database entries of a product in a multistore system: