I had a flood in my bathroom and there were two layers of vinyl tile that i ripped up because of water getting underneath. Lo and behold I have a tile floor and the glue from the vinyl is very sticky and I am not sure the best way to remove it. i have tried Goo Gone and that did not work. I have tried a wire brush attachment to a drill and that did not work either.
In a similar situation, but with smooth tiles, I used a wall paper steamer to steam the glue and soften it like that, then scrape it off with a putty knife. It was still a terrible job to remove it though, took me an hour per square meter.
In another room I gave up and just broke out the tiles as well, which was much easier. Those tiles you have don't seem to be in a good condition, so removing them might be justified for that reason as well.
MEK or methyl Ethel ketone with good ventilation and chemical gloves will dissolve the adhesive, the biggest problem is some residue in the grout. Once the tile is clean a muratic acid solution and water will etch the grout reducing any left over residue. Use a rag that is damp with MEK if you pour it on the adhesive will dissolve and really get into the grout. After etching and cleanup the grout will need to be resealed.