The changes brought about by democratisation were limited but important. Only sixteen authoritarian regimes were changed through elections by

1994. In fifteen others the single parties in power in 1989 were still in power in 2002 after winning multiparty elections. Even where regimes changed, politicians often remained the same: ‘born-again politicians’, as they were known in Malawi, who had been ousted from one-party governments, regained power through democratisation, and still saw the state as chiefly a source of personal advancement. During the first seven years of democratisation, the number of parliamentarians in sub-Saharan Africa increased by 22 percent.^22 The process was about people rather than policies or, for the most part, political structures. Not a single left-wing party emerged. Moreover, democratisation was largely an urban phenomenon. National conference delegates came overwhelmingly from the towns, especially the capitals. In the countryside, the vulgarity and divisiveness of party competition were often resented, so that old-style autocrats like Mugabe in Zimbabwe could frustrate urban pluralism by mobilising rural support. Multiparty voting was chiefly on regional lines, often exacerbating ethnic and religious tensions, and money changed hands even more freely than before. Africa’s economic and social structures had not altered sufficiently over half a century to make political democracy decisively easier to entrench than it had been at independence.

To help anyone who is reading this other than OP, that's the full paragraph on page 301 of 2nd edition of Africans; the history of a continent. In 3rd edition it's on page 305. I bolded the specific claim for clarity where it is in the paragraph.

I would say that statement is true, if Iliffe means that no new left wing parties emerged.

South Africa is a strange edge case where the Apartheid government ended the bans on African National Congress, Pan African Congress and the South African Communist Party that had been imposed in 1960 for ANC and PAC and 1950 for SACP.

So, in the 1994 elections there is the dramatic success of ANC which was a political movement which had espoused left-wing economic positions from the 1960s-1990s but had only been able to operate and organize openly since 1990.

TBH, I think Iliffe would put that to one side, and say that he clearly meant that no Left Wing parties were newly formed in the 1990s, and ANC et al were established parties. And anyway, ANC began a shift from economic positions like advocating land redistribution and economic justice towards recognizing existing property rights and market economy in the early 1990s as attaining power became likely.

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Very broadly speaking, the 1990s was characterized by a weakening of left-wing politics on the continent.

In the late 1980s there were avowedly Marxist-Leninist regimes in countries like Peoples Republic of Benin, Peoples Republic of Congo (Brazzaville), Peoples Democratic Republic of Ethiopia, Somalia, Guinea-Bissau, Cabo Verde, Angola, Mozambique. In Zimbabwe there was infighting between Maoist party ZANU-PF and Marxist-Leninist party PF-ZAPU, which ended with the latter merging into ZANU-PF.

The fall of communist regimes in Eastern Europe in 1989 and of the Soviet Union in 1991 had drastic consequences for many of the above countries. Benin, Congo(Brazzaville) saw dissolution of Marxist-Leninist vanguard parties, and move from "peoples republics" to simple republics (though communist leaders like Kerekou and Sassou-Nguessou would return to power in the late 1990s as heads of social democratic parties)

The Peoples Democratic Republic of Ethiopia (effectively the re-named Derg) would lose a civil war in 1991 against several ethnically based rebel groups under the coalition banner of Ethiopian Peoples Revolutionary Democratic Front. Ironically, the EPRDF in the 1980s stood on a Marxist-Leninist platform, while fighting against the Marxist-leninist PDRE.

But, after 1991 the EPRDF makes an ideological shift away from Marxism-Leninism to social democracy and ethnic federalism.

Ditto, in Angola and Mozambique, Guinea-Bissau and Cabo Verde, ruling parties MPLA, FRELIMO, PAIGC and PAICV shift from espousing Marxism-Leninism to espousing Social Democracy.

Ditto, the National Renaissance Movement in Uganda shifts from a Marxist or Socialist and Pan-Africanist position of the 1980s to a nationalist, economically liberal position in the 1990s.

It is fair to say that there was a sense of Marxism-Leninism being discredited on the continent with the fall of the Soviet Union, and ruling parties making concessions to the new neoliberal economic order, or going defunct.

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The other major trend that must be acknowledged is the economic and public debt crises of the 1980s, and the role of IMF loans in pushing Structural Adjustment austerity on African governments from 1980-2000.

Very, very briefly:

1. in 1960s and 1970s, many newly-independent African governments sought to promote industrialization of their economies by government spending on parastatal companies and placing high tariffs on imports, keeping the value of the currency high (to promote home-grown products over import competition). Governments also tended to spend on hospitals, bureaucracy, and food and fuel subsidies. They paid for industrialization and social spending by channeling agricultural and natural resource exports through marketing boards (effectively placing a heavy tax on farmers). They also took out international loans to make up shortfall in development budget.

2. in 1971 the US went off the Gold Standard and abandoned the Bretton Woods framework. For complicated reasons, that introduced uncertainty to international loans and bonds market. That, combined with the 1979 oil crisis triggered by the Iranian revolution, meant a sharp rise in interest rates for development loans.

3. Where development loans had been manageable part of budget in 1970s, sharp rise in interest rates meant they ballooned to larger and larger portion of African governments budgets (ditto for Latin America, Caribbean and other places). These countries faced international debt crises.

4. The World Bank and International Monetary Fund (funded primarily by US, Western Europe and Japan) stepped in as lenders of last resort, offering loans to bridge the budget crises. These loans came with a set of conditions, where IMF required recipient countries to adjust the structure of their economies (called Structural Adjustment) by privatizing parastatials, devaluing currency, eliminating import tarriffs, eliminating marketing board monopsonies, and IMF insisted on sharp cuts to government payrolls (meaning cuts to education, public health, and bureaucracy) and end to fuel and food subsidies.

These changes were frequently unpopular with the public, because education, health, and affordable food and fuel are popular. Portions of the public also saw loan conditionality as infringement on the sovereignty of African governments to make policy for themselves. Commentators on the Left saw Western triumphalism and political opportunism in the tying of foreign aid to help economic crises with conditionality that African governments institute multiparty elections. Leftists saw this as a way for the US to destabilize vulnerable Leftist regimes in Angola, Mozambique, Tanzania, and elsewhere.

But, at the end of the day, the political class of African governments came to the conclusion that there was no alternative to get out of the economic and debt crisis than accept Structural Adjustment and get the loans.

If I recall correctly, Zambia is the only country that rejected loans conditions and ended up turning down IMF loans in the 1990s.

Anyway, all of this is relevant because a new left wing party contesting multiparty elections in the 1990s would face severe questions on how to pay for social spending or how to manage economic justice in the midst of the economic crisis of the late 1980s and early 1990s. For all the outrage at loan conditions, there also was a recognition that African economies were dependent on these loans for survival. So, there was not much space for new left wing parties to advocate for economic policies that ran against Structural Adjustment enforced liberalization of the economy.