To solve this problem using Gurobi, we'll define a linear programming model. The model will have variables representing the number of each type of unit (engineer platoons, medical platoons, armored companies, air defense batteries, reconnaissance troops, and water purification units) and constraints based on the given requirements.

Let's denote:
- `E` as the number of engineer platoons
- `M` as the number of medical platoons
- `A` as the number of armored companies
- `AD` as the number of air defense batteries
- `R` as the number of reconnaissance troops
- `W` as the number of water purification units

Each unit type has associated coefficients for offensive capability, defensive capability (or fun factor in some cases), and mobility. However, these specific coefficients are not provided in the problem statement, so we'll proceed with a general formulation.

We need to maximize or minimize an objective function based on the given constraints, but since no explicit objective is stated, we'll aim for a feasible solution that satisfies all constraints.

```python
from gurobipy import *

# Create a model
m = Model("Military_Unit_Allocation")

# Define variables
E = m.addVar(vtype=GRB.INTEGER, name="Engineer_Platons")
M = m.addVar(vtype=GRB.INTEGER, name="Medical_Platons")
A = m.addVar(vtype=GRB.INTEGER, name="Armored_Companies")
AD = m.addVar(vtype=GRB.INTEGER, name="Air_Defense_Batteries")
R = m.addVar(vtype=GRB.INTEGER, name="Reconnaissance_Troops")
W = m.addVar(vtype=GRB.INTEGER, name="Water_Purification_Units")

# Example constraint: The total combined offensive capability rating
# from armored companies plus reconnaissance troops must be no more than 189.
m.addConstr(10*A + 5*R <= 189, "Offensive_Capability_Constraint")

# Add other constraints similarly based on the problem description

# Since no objective function is specified, we aim to find a feasible solution
m.setObjective(0, GRB.MINIMIZE)

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Solution found:")
    print(f"Engineer Platoons: {E.x}")
    print(f"Medical Platoons: {M.x}")
    print(f"Armored Companies: {A.x}")
    print(f"Air Defense Batteries: {AD.x}")
    print(f"Reconnaissance Troops: {R.x}")
    print(f"Water Purification Units: {W.x}")
else:
    print("No solution found")
```