It is possible that the device is simply not exposing any open ports. Thus you are not finding anything, but... port scanning is an art. Nmap has many options and there are pitfalls too.
If you are stuck at this stage, you could try something else to gain a better understanding about the inner workings of your device. Assuming it's connected to your home wifi network, you could try to sniff the traffic flowing in and out. Look at the types of traffic (eg HTTP, DNS etc) and the destination ports. Then you can start making educated guesses about what kind of software is running on the device eg an embedded webserver or something else.
For example I have a managed switch and I have configured port mirroring so that all traffic flowing through a specific port is "copied" to another switch port, and from there I use a separate network card and Wireshark to analyze the traffic.
My suggestion would be to build a small lab, perhaps invest in some equipment like a managed switch that will make the job easier. You can also build your own. For example if you have a spare Raspberry PI you can build a wifi hotspot with hostapd and then you can sniff all that you want.
Learning how to use Wireshark will be a requirement. Shouldn't be too difficult. One of the first things to know is how to set up capture filters or display filters, so as to filter the traffic to a single known MAC address, and eliminate the "background noise".
Another suggestion: since you have physical access to the device you could enable debugging mode from USB, on an Android device you would use ADB. Root the device perhaps. Once you have console access you should be able to see what's going inside the device.