I am not quite sure if Hamachi helps, but Tunngle.net does! I've already tried and tested it. It works with GTA 1 over the internet! Even if you don't have "white" IPs.
Here is how to launch it:
You need to run it under Windows 7.
Download the DOS GTA 1 version. Unpack to a folder like c:\games\gta (should have no whitespaces).
Connect to the internet with a cable. It will NOT work over WiFi.
If your computer is connected to a router, it is absolutely necessary to forward a port 11155 over the UDP protocol for your local IP. Read the instructions at http://portforward.com (this is only needed once).
Register at http://tunngle.net. Download and install the Tunngle client.
Download and install the DOSBox DOS emulator (http://dosbox.com).
Make sure that Windows firewall has all type of connections allowed for DOSBox (Start>Control Panel>Firewall, then click a link on a sidebar to find a list of all applications and permissions, look for dosbox and tunngle, too; check all checkboxes for those).
Open dosbox options (Start>DOSBox-0.74>DOSBox 0.74 Options). Notepad launches. Scroll to the end of file. You'll see a line "ipx=false". Change it to "ipx=true" (this is only needed once). Save the file and close Notepad.
Launch your installed Tunngle client app (it will NOT reliably work under Windows 10). Log in and make sure that it shows a green face icon at the bottom right corner. That means the port is open and connected. If not, repeat the port forwarding process, you probably missed something (and don't forget you can't use WiFi for this).
Launch DOSBox app. Enter the following commands:
mount c c:\games\gta
Then, the player who will be the server, in his Tunngle client app creates a Private Network.
Then he also enters the following command in his DOSBox:
ipxnet startserver 1025
Then, the player who will be the client, enters the private network room created by the server player. And confirms the authorization process on the Tunngle website (this is only needed once).
Then he enters the following command in DOSBox:
ipxnet connect 000.000.0.000 1025, where the digits between dots is the virtual IP of the server player (hover his nickname in the Tunngle room).
Then, both players enter the following command in their DOSBox apps:
GTA.BAT (or GTADOS.BAT, depending on the version).
Game launches. You select Network Configuration menu and choose IPX Network, then enter the port 1025, then choose Save settings.
Then both choose Play game>Low quality mode.
The server player selects Gather network.
The client player selects Join network.
The server player presses Enter when he sees Found a player.
Game starts. Voila!