The deeds state in favour of the owners which when written was the MOD, but it states they must not cause noise, nuisance, noxious smells etc to the owners now or any owners in the future which is now the residents of the road
If the benefit has passed from the MOD to the residents company then it should still be enforceable.
If X (MOD) owns a piece of land which he splits into two plots, selling one plot to Y (school) and having a restrictive covenant in favour of the plot he has retained, then he can enforce the covenant as long has he retains the land to be benefited. If X now sells the plot (your houses?) he had retained, he will not be able to enforce the covenant for the future, although the purchaser from X will be able to do so.
If A (school) agreed with B (MOD) that he would not use the property to make a nuisance, then if B (MOD) sold his property to C (your houses), then C could enforce the covenant against A (school). However, if A (school) sold their property to D, then C could not enforce the covenant against D.
The issue being the cost to enforce these covenants would be costly to the residents company.
As with most civil legal disputes, it depends how far you're prepared to go. You may get away with a solicitor drafting a cleverly worded letter, outlining the potential breach and grounds for taking it to the lands tribunal to be enforced. They would inform the school that a failure to win the claim would result in a financial compensation plus full legal costs. This is sometimes enough to scare the pants off people - even if you have no intentions of taking it further, you may get a positive result an the basis that the school THINK you're going to take it further. I'm sure, like all schools, they have Governors and a letter from a solicitor threatening legal action may result in the school being forced to find a more suitable location for the play equipment.