Any type of shoe can be used for running. Hell, you can even use slippers to run. However, it won't be comfortable now would it? Plus, you would probably get injured if you use them for some time.
Although Asics shoes are derived from the Onitsuka, I doubt the Onitsuka Tiger would make a comfortable running shoe. Reason being?
1. The upper part of the shoe has no mesh whatsoever. It looks like it's leather or something. Mesh is important for ventilation. Plus, it's lighter too. (But that doesn't mean light shoes are the best)
2. The outsole looks pathetically thin. It doesn't look like there's any arch support too. It would not make for a great running shoe. Maybe just a casual one.