I'm currently playing Pokémon Red on the 3DS virtual console and was excited to find that the old glitches were still in tact.
Long Range Trainer Glitch Guide
When I made use of the Long Range Trainer glitch on my original Red cartridge, I used Abra's teleport in Cerulean, but I never tried it anywhere else. I know there is another potential Mew using a north-facing Gambler on route 8, but when I tried this using teleport, when I return to the area, no other trainers will start a battle with me, and I have to reset.
The guide says to use fly, but also says teleport can be used to acquire Mew at the earliest point in the game, which I can verify. I don't know why it wouldn't be a valid way to initiate the glitch in any other area.
Best Answer
Yes, you can use any move that will take you away from the currently planned fight. Dig or an escape rope would also work as well. From the article you linked.
This is because the key to the glitch is actually triggering the Long Range Trainer with the ! above their head to initiate a battle, but not letting it start. Any method from the menu by which you can do that should work.
Of note, it may be difficult to use teleport or dig over fly mostly because of the nature of these moves. You don't get to control where you end up quite as easily as you do with fly so it would require a more planning and setup to get it to work than it would otherwise.