I wasn't lucky with that snap package either but I installed it successfully on my Solus notebook and desktop. Just build it from the github repository of ZeroTier.
Here are the steps I documented:
sudo su
eopkg install systemd-devel llvm-clang -y
mkdir /opt
cd /opt
git clone https://github.com/zerotier/ZeroTierOne.git
cd ZeroTierOne
make
make selftest
make install
wget https://raw.githubusercontent.com/zerotier/ZeroTierOne/master/debian/zerotier-one.service -O /etc/systemd/system/zerotier.service
systemctl enable zerotier
systemctl start zerotier
Now join a network using this command: zerotier-cli join networkcode