Hi. As Leo says, the website has a standard warning that you might need to re-check. I think they always include that warning as they don't track whether the various legs are with partner airlines.
However looking at the flight details and airlines, I would think you will need to collect luggage and re-check in at Amsterdam but not in Taipei (where your one hour turnaround is). However, I would have to say that, while I don't know Taipei airport specifically, there are very few (if any) airports where I would feel comfortable with a one hour connection time. Amsterdam is actually probably one of the few because connections don't have to go back through security screening again. But in most airports you do. So I would be wary of that connection.
Do you mind me asking - are you booking a return or one way ticket. The link only shows one way. The reason for asking is that the price quoted is decent for a one way but if you're booking return flights, there may be just as good prices with easier connections - one way tickets can be expensive