Final Solution(Though its already answered, I wanted to solve it on my own as a part of learning. Due to an ongoing problem with imgur, it took too long for uploading the solution)
![enter image description here](https://i.sstatic.net/EwO2a.png)
SUDOKU Solution.
![enter image description here](https://i.sstatic.net/VdBs2.png)
Updated Better solution
Upon observing we get to know that, 5-8, 6-7 and 9-7 are unique. And we get ahead like this
![enter image description here](https://i.sstatic.net/QJQi1.gif)
Solution(Getting the idea from Ivo about the marked spots in the puzzle)
I am a novice to Grid puzzles and have specified all the steps I took while solving ...
1. We can simply fill 3-5 block just by looking.
![enter image description here](https://i.sstatic.net/sMGfe.png)
2. I did a bit of a trial and errors, and I came up with the next cell as 3-9.
![enter image description here](https://i.sstatic.net/2a1m4.png)
3. Now, that we have 3-5 and 3-9, we can cross of 3-4 at the bottom as there is no other way to go
![enter image description here](https://i.sstatic.net/0bIw7.png)
4. Since we have 9-3 pair, we can cross off 9-4 at the top
![enter image description here](https://i.sstatic.net/9s59J.png)
5. Which gives 9-2 as well.
![enter image description here](https://i.sstatic.net/HihfH.png)
6. Now, we have 9-3, 9-4, we get 9-8 as a new pair
![enter image description here](https://i.sstatic.net/Wu4t9.png)
7. Also, we get 9-1.
![enter image description here](https://i.sstatic.net/99reH.png)
8. And then similarly, 9-6, 9-7, 9-5, 2-5, 4-7, 1-8
![enter image description here](https://i.sstatic.net/HF1kl.png)
9. Now, as we already have 3-4, we get 4-2 as a new pair
![enter image description here](https://i.sstatic.net/WzpKP.png)
10. Also, we already have 2-5, so we can knock off 5-1, 2-6,8-7(dead ends)
![enter image description here](https://i.sstatic.net/nvXrC.png)
11. We have 8-7 and 7-4, so we get 7-5 as a new pair. Also, we can knock off 7-3, 8-6 at the top right.
![enter image description here](https://i.sstatic.net/JfKgW.png)
12. We already have 7-4, 7-3, so we can knock off 7-6 which also gives 3-8, 5-4, 2-3 as dead ends
![enter image description here](https://i.sstatic.net/pG6oW.png)
13. Now, we have 8-7, 8-3, so we can knock off 8-4 which also gives 1-6, 3-6 as dead ends
![enter image description here](https://i.sstatic.net/OTCuj.png)
14. We already have 8-4, so we can knock off 4-1 which also gives 8-2, 6-5 as dead ends
![enter image description here](https://i.sstatic.net/9jhJa.png)
15. Now that we have 1-8 already, we can get 1-7 and then 1-3 at the top. Which gives 7-2, 6-4, 5-8, 1-2 as dead ends and completes the Domidoku.
![enter image description here](https://i.sstatic.net/ELrww.png)
BRAVO!!