So the Amcrest camera can store recordings and snapshots on a NAS, but it's very unclear how this needs to be setup from looking at the WebUI of the camera.
So some searching finally made me find this description (link) and I'm just posting it here for future reference and/or as a backup.

Short version: It uses a NFS share ... (would never have figured this out by myself)

Long version:

QNAP / NAS

To allow Amcrest cameras to connect to QNAP via NAS connection you will have to enable NFS in the Network and File Services located in the control panel of your NAS. For more information on how to do this, please refer to the information provided below. 

Note: QVR and QVR Pro support most Amcrest camera's as well. Worse case as ONVIF camera's.

Step 1: Please open Control Panel and navigate to Network & File Services > Win/Mac/NFS.

Step 2: Click NFS Service in the new window and enable NFS v2/v3 and/or NFS v4.

Step 3: After the services have been enabled, follow the link “Click here to set the NFS access right of the network share”. You will be taken to the Shared Folders menu.

Step 4: Under the Action column, please click on Edit Shared Folder Permission.

Step 5: In the next window, select NFS host access under Select permission type.

Step 6: NFS access right is disabled by default, here you can enable it first.

Step 7: Click the Add button to add Host / IP / Network and to set their permissions

Allowed IP Address or Domain Name

1. Single server: A valid domain name, hostname, or IP address that can be resolved by a DNS server.
2. Use wildcard characters to specify a series of servers: Use “*” or “?” to specify the string criteria. When you use wildcard characters in a valid hostname, dot (.) is not included in wildcard characters. For example, when you enter *.example.com, one.example.com is counted while one.two.example.com is not counted.
3. IP network: Use a.b.c.d/x. a.b.c.d refers to the network and x refers to number of bits of the network mask, for example, 192.168.0.0/24. Another valid format is a.b.c.d/network mask. In this case, a.b.c.d refers to the network and the following value refers to the network mask setting. For example, 192.168.100.8/255.255.255.0.
4. If using IPv6, enter the IP address and prefix length (ex: 2001::208:9bff:feed:5023/64) for filtering devices and permission settings. If the prefix length is not set, it will refer to a single host IP.
5. Network group: Represented as @group-name; group-name refers to the name of NIS network group.

The Host/IP/Network field will be the local IP address of your Amcrest camera. Please make sure the permission is set to read/write and the squash option is at Squash no users.

Hit Apply after you have finished setting everything up.

IP Camera

After setting up the NFS rule you will need to enter the IP address of your QNAPdevice into the camera's NAS configuration. To do this you will need to access the camera's web user interface (web UI) using a web browser. 

Step 1: In the web UI, click on Setup>>Storage>>Destination and click on NAS in the Path tab. 

Step 2: Click on the NAS tab. Enter the NAS server address and make sure you specify the volume and the folder where the recordings will be sent to. As shown below:

Click Save. 

The events from your camera will be stored in the file station of your NAS. 

This works in a similar way for other NAS devices (Synology for example).