The generic way to do that is to group the desired fiels in a tuple, whatever the types.
df["Rank"] = df[["SaleCount","TotalRevenue"]].apply(tuple,axis=1)\
.rank(method='dense',ascending=False).astype(int)
df.sort_values("Rank")
TotalRevenue Date SaleCount shops Rank
1 9000 2016-12-02 100 S2 1
5 2000 2016-12-02 100 S8 2
3 750 2016-12-02 35 S5 3
2 1000 2016-12-02 30 S1 4
7 600 2016-12-02 30 S7 5
4 500 2016-12-02 20 S4 6
9 500 2016-12-02 20 S10 6
0 300 2016-12-02 10 S3 7
8 50 2016-12-02 2 S9 8
6 0 2016-12-02 0 S6 9