If Mormons are Christians, why do they try to convert other Christians?

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Mormons try to convert other Christians, as do evangelical Protestants (very successfully) and Roman Catholics (not so successfully) - because in the West most people are weak or lapsed Christians, and form the main missionary field.

So converting other Christians is something which all evangelizing denominations do.

And for very good reasons.

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What tends to happen is that a lapsed, feeble or 'in name only' member of a Christian denomination converts to another Christian denomination with an increase in faith, zeal etc - as when an ex-Roman Catholic is 'born again' - and I would regard this as usually a positive matter

In sum: surely, to take a feeble Christian and convert them to a stronger Christian is - usually - a Good Thing.

This process may, often does, include a change of denomination, which will have disadvantages - but may in practice be necessary.

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But there is a difference - because quite often evangelical Protestants or Catholics covert other denominations for the sake of their salvation - they believe that their denomination is necessary for salvation. They may - in all sincerity - warn the potential convert that if they do not convert they will be damned. This may indeed be the major pressure for conversion to mainstream Christin denominations - powerful negative sanctions against those who fail to convert.

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But Mormons do not believe that.

Mormons believe that devout members of other denominations are already saved, but that becoming an faithful and active Mormon may enable them to attain a higher level of exaltation - i.e. salvation to a higher degree of Heaven - or at least start them along that path in a process which may continue after death.

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So Mormon missionaries, unlike most other Christian missionaries through history, are not threatening with Hellfire or else; but are instead are offering an add-on (as it were) to other forms of Christianity.

But Mormons do not regard Christians of other denominations as damned - merely limited to a lower, but still wonderful, level of Heaven.

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(Indeed, the sanctions against not being a Mormon are even 'weaker' - or kinder - than the above simplified account - because Mormons believe that spiritual progression may continue after death - so that after death a person may attain the higher levels of exaltation, even if they do not become a Mormon in this earthly life. The exaltation benefits of being baptized a Mormon accrue almost entirely to the most devout Mormons, whose marriages are sealed for time and eternity in a Temple, and who live according to the commandments and by the rules of the LDS church. Devout Mormons who do not attain this high level of active practice are in much the same salvific situation as devout non-Mormons - will go to the same high but sub-optimal level of Heaven.)

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So Mormons are pretty much offering only positive incentives to the potential convert.

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References: 

https://www.lds.org/topics?lang=eng

http://eom.byu.edu/