Learn German: Eine Phiole dieses Giftes kostet tausend Euro. - A vial of this poison costs a thousand euros.

In German, when a noun of quantity like eine Phiole is followed by a material noun, we usually use an apposition where both nouns share the same case, such as eine Phiole Gift. However, because the material noun in this sentence is modified by a determiner (dieses), we must use the partitive genitive instead: eine Phiole dieses Giftes.

How would the phrase change if it were just "a vial of poison" without the word "this"?

You would drop the genitive and use a partitive apposition. Without a determiner or an adjective, the material noun (Gift) simply stands next to the quantity noun in the same case. The phrase would just be eine Phiole Gift.

Why is it tausend Euro and not tausend Euros?

Masculine and neuter units of measurement and currency do not take a plural ending when used after a number. Since der Euro is masculine, it stays Euro for plural amounts. This contrasts with feminine units, which do take their plural endings, such as zwei Tassen.

Why is tausend not written as eintausend?

In German, you typically just say tausend for one thousand, and hundert for one hundred. You only use eintausend or einhundert if you need to be extremely precise or want to heavily emphasize the number one.