I'd like to tell you that the new Two Dots Level 72 was easier, that version 2 is a relief from the pain some experienced with the long path of the previous version... but I can't. In fact, the new Two Dots Level 72 is so hard it might be the hardest level in the game! Grab your horseshoes and rabbit's feet, and read on for more details.
Harder is the new hard
In what seems like a trend, an update to the game (Version 1.1.2) made Level 72 much harder. The old Two Dots Level 72 was still challenging, but in a fun, puzzly kind of way - and I could routinely beat it in one or two tries after I figured it out. The new Two Dots Level 72 gives you far less moves to complete a totally different board where there is much more Fire, and you need to release an almost impossible number of Anchors. Even though I respect the developer, I'm a bit at a loss for the motivation in this ground up redesign beyond making the level an implicit paywall, and that is disappointing.
...but we Match on
Like any Two Dots level, Level 72 is not impossible, but with the few moves you have, every one must count. Work your way toward the bottom efficiently. When given the choice, try to always choose the match which eliminates the most Fire Dots at the same time (with some caveats below). Despite the distraction of Fire, this level, like most of them, is really all about making Squares. You must make a ton of Squares to win this level; there is pretty much no other way. Weigh each move carefully as it is sometimes better to make a "sacrifice" move to the Fire to set up a Square, so that you can create more Squares in later moves. Keeping a good rhythm of Squares going will reduce the number of colors on your board - which will make the level beatable, but just barely.
Pro Tip The starting board always includes 3 Squares. Pay close attention to the colors, and check out the single Dots that are touching Fire. Start by making a Square that's the same color as one of the Dots touching the Fire, and keep in mind the colors of the other Squares for future single Dots that touch Fire in your early moves. It's often good to use the middle Square in your second or third move, because otherwise it can get jumbled as you clear Fire Dots below it.
Pro Tip Anchors will not start to fall from the center until you clear the initial Anchors on one side or the other. In my experience they seem to fall sooner if you clear the Anchors on the left side first.
Warning As you near the bottom, your moves will eventually split the Fire. If you split the Fire in two pieces, two new Fire Dots will grow on the next turn. This means it can be better to make a sacrifice move rather than splitting the Fire, since letting two Fire Dots grow may cost you two turns to recover from.