Is there any way to play Tekken 3 multiplayer online?
Solution 1:
I don't know of any other way than emulation to achieve that. Emulation is simulating an electronic system on another one, in that case running a software imitating a PlayStation on a computer. Emulation is legal when you own a copy of the game.
I recommend to try Romstation. It is an emulation manager, usually working pretty well out of the box. It comes with the most popular emulators for many consoles, packing everything in a nice interface.
The key feature is online play : RomStation has already a fully configured space to play online, available for many games, including Tekken 3.
You also might be able to find other persons willing to play online with you, searching the internet for dedicated forums.
Solution 2:
Without emulation, no.
Tekken 3 was exclusively ported to the original Playstation which had no internet access. Most fighting legends were re-released on XBLA or PSN, but sadly there were no old Tekken games re-released on Xbox Live and the ones released as "PS1 Classics" on Playstation Network had nothing added, not even online play.